I just want to jump in and say that while it is totally true that guildhopping might be a good way to climb your way into a top guild, it is absolutely not required if you find a guild that needs you and you write a great app. I'm the raid leader of a high ranking guild and we give opportunities to players from much less progressed guilds all the time. You need to really sell yourself - think about what makes you a great player, what you can offer a top guild if they give you the chance, and what makes you better than the people you raid with. Don't focus too much on your normal mode parses. Mention them, sure, and point out that you're doing all you can, but focus on the player. Sell yourself as someone who will be there every night, who can pick new fights up quickly and even play new classes or specs if needed, someone who does research outside of raids, who will read theorycrafting discussions on the forums and be engaged in strat development. Find the balance between ambition and knowing your place. Every top guild wants dedicated, skilled players who are still willing to sacrifice for progression by sitting when needed or giving up loot or whatever else is needed. The team is everything.
If you can be that player, your progression history doesn't necessarily mean anything. Of course if you've killed everything pre-nerf since Sunwell that's a huge plus but you only have to be a great player. Gear is easy to come by these days and experience is a bonus, nothing more.
Best advice I can give you if you think you can cut it and you want to be in a good guild is just to app to one. App to the guild you dream of being in and then if they don't have room, persist. If they still won't give you a shot, try somewhere else. Don't sell yourself short if you don't have to.
As a recruiter for a top200 guild i can give you some insight. I mostly just skim over most of the answers in application, after reading thousands of those they all look the same anyways, also past tiers experience is overrated. What really matters is logs (i ask guildies of specific class/spec to review them to detail) and i will usually talk to your ex GM/raid leader about your personality.
As for joining top10-20 guild, i'd advise against that before you get some experience in level just below that, i doubt anyone would be able to jump right in and perform on required level.
1) I'm not one to advocate guild hopping, personally, especially if your actions can easily be seen as guild hopping. One of the standard questions on any app (ours included) is "list your past 3 guilds and why you left them," and we will check up on them, especially if you say "I'm leaving for personal reasons." You're okay on this front, it seems, because it's not personal but "professional," you think you can do better, you are ambitious, you want to achieve. The stepping stone guilds don't like to be stepping stones, and the top guilds don't like people who have the stench of only being in it for themselves. Recruiting is a tiring routine for any guild, they're investing in you, and they'll be wary to invest if you're going to take all the training and equipment and bounce after a few months.
2) Consider a realm first guild on a medium server (somewhere in the 70-100 range on the server list). They're generally desperate for people to transfer, and if you can find a solid one, what you'll find are good players who are loyal enough to stay on a dying server because it's where they rolled up on. On smaller servers, too, good rises to the top a lot quicker so it's likely you'll be playing with all the best players on the server. On a large server, or in a highly ranked guild, they have an infinitely larger recruiting pool so it's much harder to get your foot in the door there. An 8-10/16H guild on a medium-to-low pop server will be easier to get into than a 4/16H guild on a large server, in general - especially as the tier gets along and 8-10/16H is much more prevalent.
3) As a paladin, know either prot or holy backwards and forwards (holy is better probably, as tanks are establishment in most guilds, and generally a 25 man will have a dedicated DPSer who becomes the 3rd tank when they need one). If you can be the clutch hpally they need on a fight, that makes your app stronger.
4) As a paladin, know your buttons backwards and forwards. As an example, paladins would be expected to know when/be expecting the call to use Hand of Protection on fights like H-Gara'jal (on the tank), H-Blade Lord for Wind Step, etc. Know when to use it. LoH on a fight like H-Gara'jal if you're going downstairs, also a thing to know. Bubble on many fights where paladins are good for a one-time-every-5-minutes soak (we use our pally to break cobalt bombs when "overrun" on H-Stone Guards - I'm actually under the impression he does it just because he's bored, we also use him to soak a bunch of sparks on H-Will). Know how to layer any mitigation CDs you have when you need to - DP, any self-healing (idk how paladins have changed since Cata so I don't know the mechanics behind Selfless Healer any more).
5) Don't talk much during trials - but don't be afraid to ask ret pally specific questions pertaining to specific fight mechanics. This kind of ties into researching and knowing the fights the guild is doing before you app, but if they explain the strat generally, ask them if they want you to BoP a Wind Step bleed off a caster on H-Blade Lord if they don't mention it. But only do that if you can do it perfectly - no excuses. Recruits that have impressed me the most in the past are the ones who 1) do what's asked of them without arguing the strat, and 2) offer to take on additional responsibility beyond what's asked of them, and 3) execute all of it. The last guild I joined, I joined during Firelands after 3 years with my previous guild. I was 6/7H and they were 7/7H (pre-nerf). They told me what they did in the fight I hadn't downed (the strat was generally universal for H-Rag), and then I asked if they wanted me to a) be the guy who knocks back the meteor on my side, and/or b) clear dreadflame in p4 (as a hunter). After a short pause, they said sure, clear dreadflame in this area. After performing respectably on DPS on a very MM-unfriendly fight, I then executed dreadflame perfectly even though I'd never done the fight successfully before, because I had researched the fight extensively and had some very brief practice with my previous guild on the few p4 attempts we had gone through. My trial was a breeze after that. If a recruit makes our farm clear even easier by throwing in a BoP on a Wind Step bleed that we previously didn't have - that's a recruit that's made an impression.
Just jump on it and apply to guilds you see fitting. Climbing the latter will likely only delay you are perhaps block you from ever getting into those guilds you really want, due to showing tendencies of lack of loyalty/guild-hopping/loot-whoring.
Make a good application and that should be enough for a serious guild to give you a chance. That's how we did it atleast, and that's also how I went directly from a underdog-guild and into a server first one back in the days. I am sure this mentality haven't changed. In fact, your odds are probably better today than it was for me when I did it, as gearing is a lot easier to get on pair with the rest these days.