Hi guys. I have searched high and low on here and other threads for an answer, but have not found one.

I have a Brooks B15 saddle on my 1980 Schwinn Varsity. The saddle is quite slim and narrow. It is slim and narrow enough that the bolts on the rail clamp are slightly exposed and have worn holes in my jeans. I would like to replace the clamp with something a bit slimmer, whether it is with vertical mounted bolts or side mountain allen bolts.

I believe I have the 13/16 seat post with the standard rail clamp.

Can anyone link me to or suggest a post or rail clamp upgrade that will work? I'm happy to buy a whole new post if need be.

Interesting question for your first post. Welcome.

Could you cut the bolt down on both sides so they do not stick out that far? To buy a different post and change out your clamp arrangement, you will first have to measure the post and then see if that size is available.

It's the standard 13/16 7/8" post. I'm just can't find a post that doesn't require me to use the seat clamp that has the two bolts on the side. It seems there are many seat posts that have the vertical bolts, but none of this size--at least that I can find. [h=1][/h]

It reads to me that the stock clamp designed for a larger post ( the varsity / continental posts essentially the same as the other electro forged frames and quite small in diameter ) the nuts just run down on the clamp to get it to cinch.
Way back at Schwinn shops some saddles came with two central clamp parts for the two basic diameters of post.
Some used a collar about 340 degrees in circumference to make up the gap.
As the saddle clamp bolt most often has a square center section, trimming off the excess might work, but I have a feeling you have a basic mismatch of parts, a collar might be the best route. A local bike shop that used to sell Chicago schwinns might be a place to look.

replace the seatpost with an aluminum one with a one-bolt clamp.

That's what I would like to do, but I don't think a seat post or one bolt clamp exists that fit the Varsity. Can you link me to one?