Can't help you out with tips for building the kit; I've had a few Hasegawa Eagles (including the first release with the ASM-135) but never did build any.
As to the actual ASAT birds, there were at least two aircraft involved in the testing; 76-0086 and 77-0084, both F-15A's. I dunno if they were the only aircraft to be used, however. I believe both were aircraft of the 6512th Test Squadron from the AFFTC (Air Force Flight Test Center) at Edwards AFB.
Only one actual satellite was ever targeted during the test program, being successfully destroyed.
Here's a couple links with more info, some of which is, unfortunately, contradictory. There's several photos to be found on these sites, although some of the more tantalizing shots (especially those of the port side of both aircraft) are rather small.
Air-Launched Miniature Vehicle (ALMV)
ASAT - This is a page from the Vought website.
The Death of a Satellite: Edwards AFB
Vought ASM-135 ASAT
F-15 ASAT - This page has info only, no photos.
Here's a larger image of 76-0086:
The 48th FIS at Langley AFB in Virginia and the 318th FIS at McChord AFB in Washington each had several airframes which were wired for the ASM-135. None of these aircraft ever carried, much less fired, an ASM-135. (Despite what Tom Clancy says!
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