Train through HIM, or taper and rest?

Depends on your goals for the HIM, I'd say. Is it your first? Are you looking for any particular time goals? I'm in pretty much the same situation and I'm not doing much of a taper for my HIM (although that's partly because I'm also training for a marathon three weeks after the HIM in addition to the IM on August 1). I've been doing IM base building since early winter, though, so no temptation to panic about the IM being 15 weeks away...yet.

Do what you are doing.  Your HIM training is plenty for IM "base building".  Taper and rest and then start your IM training fresh. 

However, unless you feel the need to do so, there is no reason to cut back from what you are doing now when you start the IM plan.  Remember those plans are generic and don't take into account your specific situation.  Personally, I think an IM-specific plan of about 12 weeks is plenty assuming you are training regularly at a solid level before you start.  FWIW, that is roughly what I am planning with a late-May HIM and an early-Sept IM.

I am no expert. Answer depends on few things. How iportant is HIM race to you. How well do you want to perform.
Keep in mind that if you do a short taper (ie. 5 days), race, 5-7 day recovery and I emphasize recovery here, you are looking at another gain in fitness just from the race. But you have to allow your body to recover and compensate after the race. Impatience with recovery here will lead to digging a deeper whole than you want.
You are looking at HIM also as an endurance and mascular endurance training toward your IM. You are also looking to test pacing, hydration, equipment and fine tune for your IM. A lot to gain from a short taper, race and recovery.
The only thing you stand to loose is a little volume that is being offset by higher intensity. I have gathered from literature that volume (as long as you are within ball park) is secondary to quality workouts. I belive that a well raced race represents that. Now go out there, taper let 'er rip, recovery and move on.

Thanks for the replies everyone.  Very helpful.  Looks like I'll stick with plan A.