14-28 freewheel - swap for 32?

Nice.That should now last for the rest of your riding!
Cheers,
Pete.

You'll probably have an easier go with a cassette since shimno hyperglide cogs are still pretty available , unless it's the old uniglide cogs. Your LBS should be able to figure that out which system you have before you start looking. Sheldon Brown has great info on his website to make it all clear.

Cheers, 
Michael

Thanks both - Just been having a look at Sheldon Brown. It's a uniglide - so only chances are lightly used or NOS that have been sitting around since early 80's? And to find a 32tooth might be even harder than finding that Suntour NOS screw on one.
I had no idea about this system.
Thanks for offer Pete - I will weigh up my options and think how I might progress.

Another question - I was getting a bit of slippage on the old block (that, and the desire for a few more teeth to make hills slightly easier put me on this path) . Does this now seem more likely to have been the RD or can these uniglide blocks cause a slip too?

My 600ex and the old Aerospace 400 both have / had UG cassettes. IMHO, if you're only running six speed they are better than HG for the reason that Pete said. And they're a bit more rugged anyway. Availability is reasonable on eBay or try a general or retro bike forum. If it's not obvious, the smallest cog is threaded and holds all the others on. You will need two chain whips to get them off - one to hold the cassette, the other to unscrew the locking cog. UG cogs fit on HG hubs but not the other way round - unless you file out the small slot: which would be an option so that you could use the more commonly available HGs. Note that HGs are supposed not to be interchangeable and must be put in the correct orientations for the best shifting. If you're bothered.

Thanks for that link.

Sorry if I sound a bit clueless here but, will each cog disassemble from the group for this kind of single cog replacement?
eg this 34t cog could be a replacement for my single 28t cog?
www.loosescrews.com/Gears/Loose-Cassette-Cogs/Shimano-Uniglide-Cassette/Cassette-34T-Uniglide-Cog-600-EX-Black-SH-3573432.html

If so, what tools are needed?

Although I think the spec sheet for my Deore RD says it recommends 32t as largest it can handle but will check again.

Thanks all.

That was quite a steep learning curve, but I think I have the hang of it now John, thanks for that explanation.

+1 to Pete for the advice on spacers. There's a 32 tooth UG cog on eBay as item 271777446954. In the US so cost inc p&p might be more than you'd want to pay.