Do not lap shims bro. Make sure your measuring right for one thing, but any machine shop will just adjust your valves with a valve job retaining all the original shims (go get shimless buckets from pick n pull for 5 dollars) and you surely need a valve job like every other 100k mile plus head does
Not sure where you got the suggestion of lapping shims, but you're right, nobody should do that if there's any other way. But if there's no other way, machine the inside face that goes towards the bucket, not the side that faces the camshaft.
I disagree about 'any machine shop' will adjust your valves. I'd phrase that as 'any machine shop' will take your money and pull the valves out and put your parts against spinning machinery, but whether or not that results in a decent valve job or correct valve lash values is far from guaranteed with 'any machine shop'.
When looking for a good machine shop for cyl head work, I like to start by talking to sportbike shops and Honda guys and see who's doing their cylinder head work. Any shop that can deal with Ducati heads or B/K series Honda heads and get it right the first time will absolutely get a 7M or JZ head right as well.
Also, most Suzuki GS1100 and other Suzuki/Yamaha shims that I'm aware of are 29.5mm or larger, and not compatible with any JZ or M series engine. There were some older 80's and early 90's Honda bikes that had compatible shims for 7M's, but the exact models and years escape me right now. I know they're old and hard to find now, and that Honda's shim selection range didn't really match up because they tended to be a lot thinner than what we needed.
The junkyard shimless bucket suggestion is a non-starter as well, because we're talking about a 7M-GTE. The junkyard-find 1ZZ-FE buckets work in 2JZ's, but 7M's are much smaller. To go shimless with later Toyota buckets in a 7M you need to source 1SZ-FE/2SZ-FE buckets, and that's the 1.0L & 1.3L engines found in some JDM and global market versions of the bB, Echo, Vitz, Platz, etc.
Those engines were never brought to the US since we got the 1NZ 1.5L instead in the Echo, misc Scions, etc.
So there's no US junkyard shimless 7M option that I've ever heard of or seen. It's also worth noting that any inner-shim or shimless option that works for the 16V 4A-GE will also work in the 7M-GE or GTE.
Here's a list of Toyota part numbers for the various thicknesses available in the 1SZ-FE shimless buckets, from a 4AG centric website. Just in case the OP wants to splurge on a 'buy once cry once' solution. Prices run about $9 each, which x24 valves and the shipping isn't a super cheap option. But it's an option.
Valve Lifter Tuning by 1SZ-FE parts for the 16V 4A-GE - Club4AG
The values are in mm and include the thickness of the shim
and the bucket. So you'll have to measure bucket thickness combined with each shim to properly cross reference these values. Using a dial caliper, you can use a 'tare' bar of sorts. I have a valve stem from a bent valve that I cut to exactly 25mm for this purpose; I insert that into the middle of the bucket as if it were assembled on a head, measure the total thickness with the shim and bucket and stem together, and subtract the 25mm to get the total thickness of the shim and bucket together.
Neil, I know you're trying to help and thank you for that - but please verify your information, and be very specific about exact model years/etc if you want to provide meaningful guidance. A lot of the stuff you post isn't very accurate.