I am looking for a third offensive gem.
After BoT and Enforcer is BoP really the next best offensive gem for Inna?
I hate BoP its so boring and bland.
BoT, BoS, and Enforcer are the optimal ones.
Sorry I should have clarified better.
I am not at a point where I need stricken yet.
Does that mean BoP is going to be the next best option?
Unfortunately. Due to the way the build works, there are not a lot of options that make sense. I’ve seen some suggest stupid ones so they could “diversify”.
How can BOTP be boring?? You don’t even have to level it to max to get super multiplicative damage and mitigation from it. With Trapped you’re trapped into getting it as high as possible and also make sure that that the conditions for it to work are met. With Enforcer you’re en-forced to get it as high as possible too… and dependant on your pets to do the proper work. 
Two thoughts for the speed content that OP is asking about;
Firstly, is Molten Wildebeest an option for protecting Squirt’s? I think PoJ runs that, and that build has a similar problem where it only has 2 rly good gems.
Second, something I’ve been thinking about already; for a build that hits constantly like Inna, wouldn’t BotS stack up hella fast and be super nice everywhere?
I don’t run Squirts for Inna, I run Endless Walk. The set bonus works much more synergistically with the build.
BoS does but it shines best after 5 or more seconds of build up. For speed runs where you’re destroying things for quick mats or leveling low gems, BoP edges out an overall but not by much. If you’re packing high paragon and ancients, you’ll probably not notice a difference.
Honestly, it depends on what youre doing to be honest. Some like Gogok. Some like BoP. Some like Iceblink. Me personally, i use BoP mostly.
the elite damage on bop is a big deal for inna
It really depends which ally you are running for speeds. Normally it would be water ally which att spd tick increase from gogok has lower return on dmg vs other options.
GR speeds diversify between Inna Reach / Ingeom + Echoing Fury and Shenlong with Shenglong miles ahead of other spec. With Shenlong speed, you d like either molten gizzard + ephiphany or serenity + zeis stone which is slight more efficient than molten + gizzard. With Inna Reach + other forms, difference beteen gizzard/powerful is marginal and personal. Gogok isnt an option for water ally.
Due to soul shard theme (dreg of lies rank 3 CD on elite kill), fire ally for speed is viable. With fire, gogok can be an option but in general inferior to zeis / gizzard versions my from s24 - s29 monk speeds.