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I've never had this problem, but here I am.

I recently acquired a mid-70's Olds fiberglass sousaphone that had been sitting in someone's attic for multiple years. First thing I did was take it to the shop to have the slides unstuck and get the pads and corks replaced. They did a great job.

However, now my slides, especially the main tuning slide move too easily. The main slide is right under my right arm when I'm playing and if I bump it at all it slides all the way back in. It seems like even from the factory these slides weren't tightly fit.

Suggestions on what I can do about this?

A really thick slide grease might be a a good temporary solution. I think hetmans has a slide grease specifically for loose slides, as do some other companies as well. Might want to look into that.

Indeed they do... from http://www.hetman.com/products.html

9. ULTRA SLIDE GREASE - A unique slide grease of extra-heavy consistency designed primarily for instruments with loose fitting slides. Perfect alternative for vintage instruments with corroded slide tubes

However, it doesn't look like I can actually buy it anywhere.

I'll try this UltraPure Heavy slide grease. According to Amazon comments, looks like it's suitable for this purpose.
https://www.amazon.com/UltraPure-UPO-HE ... 005MKPM1A#

You can have your tech slightly expand the slide so that it moves normally. This is relatively easy to do and very inexpensive.