The lifters should have a slight convex shape to the bottoms of them - they should not be surfaced to a flat state. It sounds like he has a set of used lifters - which could explain the large differences in length.
Lapping: This procedure can't be used to tighten up your clearances - it is only to fine tune the sealing surfaces, not anything more.
As many noted: I'd be suspect of the whole valve train setup:
a) Spring heights need to be correctly setup - such that you have the correct amount of pressure on the valve seats. Using Chevy valves makes this a bit more difficult - but there are plenty of ways to deal with it - depending on the combination of lifter types/lengths, shims, retainers, lash-caps, keepers, etc..
b) The lifters should be newly resurfaced - or new. Unless the bottoms of the lifters are practically new (and convex) - you probably do not want to reuse them "as is". I would not - it is not worth saving a few bucks in this area.
c) Machine Shop: The comment about "not being hard enough" would worry me. Seems like a way to sell you more parts and/or work - has nothing to do with Chevy valves. Truth be told, the stem ends have a lot more pressure and wear tendencies with a rocker arm, than a direct tappet on a flathead.
If it was me - I'd find a much better machine shop and ensure that everything gets done by experienced flathead folks.
Punting: If you have the capabilities and equipment to measure and set spring heights, you may be able to use the same valves, same guides and change the lifters to adjustables . . . but that is a big assumption on my part. It is really important to know what your current spring heights/pressures are - before thinking of that approach.
Best of luck . . .
B&S