I have a '99 savage, it has 18K miles on it and some change.  The exhaust baffles have been completely removed from the stock pipe (a po did that, and as far as i know, nothing else).  When I get to the top end of the rev range the bike stumbles (it cuts out badly).  Am I just running up against the constraints of this particular type of engine?  

All of my experience is with inline 4's.  At 75 mph in 5th gear, this bike is giving it's all (and then falling flat).  Do I just need some carb love and a rejet, or is that all there is?  I just got back from a ride with a buddy on his '92 FZR1000; I don't expect to out perform him, but on this leisurely of a ride, I do expect to at least keep up.

 75 in 5th is about 5400rpm, 6500 is max (90mph) you shouldn't be cutting out badly till past 6500rpm.
 You could try a bigger main jet, maybe a 150 or a 152.5.  If that makes an improvement you may want to do the spacer mod too.  With the open muffler you have, freeing the exhaust flow, you might free the intake flow to match, with a foam or k/n filter.
 You might also check the valve adjustment.
 From there check compression and timing chain.
 If you don't see an improvement maybe your just pushing all she's got.
 No matter what, you won't keep up very well over 75mph with a 4cyl. 1000cc.

Yup, acceleration above 70mph is slow coming on, but my '99 will push 85mph with my 250+ pounds. Yours should get there too if set up right. I haven't checked the jetting, but it has a HD Dyna muffler with modified baffles, and it also has the biggest Dunlop 404 that will fit on the back, so the gearing is tall. When my speedometer gets barely over 80, I figure I'm probably going 85+. Sure putts along nice at 65

I don't think I'll go with a chain conversion on the '87 until I try the big rear tire on it too. I've already got a Cheng laying around here that is a tiny bit bigger than the Dunlop. Hoping that may solve all of its high revving on the highway, but it is gonna make first gear kind of tall on the 4-speed.

Your "bad cut out" at top end is a sure sign of something amiss. Read your spark plug. Jet accordingly. Hope nobody burned anything up running it too lean.