Why don't we ask a different question here: let's say we have these dead-time cycles where we can't get the full benefit of a channeled Invocation. How many full, uninterrupted cycles do we need to make up for that?

The answer is not many. Let's say the overall damage multiplier of Invocation for an abbreviated cycle is 1.15*s/(s+3), where s < 60. The damage multiplier of passive Incanter's Ward is always 1.06. We get a table like this:

Code:

Uptime Invo IW
5 0.7188 1.06
10 0.8846 1.06
15 0.9583 1.06
20 1.0000 1.06
25 1.0268 1.06
30 1.0455 1.06
35 1.0592 1.06
40 1.0698 1.06
45 1.0781 1.06
50 1.0849 1.06
55 1.0905 1.06
60 1.0952 1.06

Note that the breakeven point is about 35.3 seconds.

Now, how many full cycles N do we need to recover and break even with IW, for s < 35.3 seconds? We can setup a simple equation to answer this question. Let I(s) be the Invo multiplier, and W = 1.06. The equation is then

Code:

63 N I(60) - (s+3) I(s) = W (63 N + s + 3)

Solving for N yields

Code:

N = [W - I(s)][s+3]/[63{I(60) - W}]

A table of these values is given below.

Code:

Uptime Invo IW Breakeven cycles
5 0.7188 1.06 1.23
10 0.8846 1.06 1.03
15 0.9583 1.06 0.82
20 1.0000 1.06 0.62
25 1.0268 1.06 0.42
30 1.0455 1.06 0.22
35 1.0592 1.06 0.01

TLDR: a single abbreviated Invocation cycle almost always breaks even with passive IW after one full, unabbreviated cycle, or two at the most. And that's all before considering haste.