Transitioning from Normal to Heroic HFC Cache

[GiveGrandmasterPlz]

I'm posting this question here since neither I nor my guildies knew the answer. Hopefully someone here at MMO-champ either stumbled across the answer via trial and error or heard about it elsewhere.

So, I'm in an odd position regarding the HFC caches. I put off my cache mission for a bit due to my dislike of the shipyard. My previous guild was a heroic guild, so I've received only a normal cache mission. Meanwhile, though, I moved into a better-progressed guild and I've gotten enough upgrades from crafting + raiding that running my normal cache mission (and suffering the two-week cooldown) isn't likely to be efficient. If I keep killing heroic HFC bosses as I have been, will the HFC cache mission automatically upgrade itself to heroic-level without me having "gotten rid of" the original normal mission first?

[Saintlel]

I'm posting this question here since neither I nor my guildies knew the answer. Hopefully someone here at MMO-champ either stumbled across the answer via trial and error or heard about it elsewhere.

So, I'm in an odd position regarding the HFC caches. I put off my cache mission for a bit due to my dislike of the shipyard. My previous guild was a heroic guild, so I've received only a normal cache mission. Meanwhile, though, I moved into a better-progressed guild and I've gotten enough upgrades from crafting + raiding that running my normal cache mission (and suffering the two-week cooldown) isn't likely to be efficient. If I keep killing heroic HFC bosses as I have been, will the HFC cache mission automatically upgrade itself to heroic-level without me having "gotten rid of" the original normal mission first?

Didn't work like that for Highmaul, I killed the threshold for heroic with a normal cache sitting there and it didn't change until I completed it and waited out the CD

Idk if the shipyard is different but I doubt it