The only real issue without having TSOH/TTIS is AD compliance. And major repairs/alterations should be on 337s available from the FAA. Minor repairs/alterations (ie MX sign off) log entries can be thrown away after 1 year.. also no one cares that the oil was changed in 1974.
If the data plate is good and you're going to use it as a CORE (as in credit towards a new engine) then its up to the shop if they want to verify if certain parts are installed/replaced per AD.
If you OVERHAUL an engine you get new logs, and all ADs start from 0 as its a zero time engine. If its a top, or IRAN, than you will need to research and comply with all ADs and even though the TSOH is NOT reset, you have completed list of ADs and the date and 'new' (basically made up) time to start with. Most recurrent ADs are based off of X hours to repeat (50,100 hours etc) NOT at a specific hour (at 2500 TSOH you must...) and even if there were ADs like that on your motor, you simply perform them while its in OH/IRAN.
The only reason people start clutching pearls when there is no log book on a CORE engine is to knock down the price. Yes, ADs need to be complied with but if its a CORE that will be IRAN/OHd then AD checks will be completed and complied with.
So its a minor inconvenience, but not insurmountable.
About the only kinda sorta gray area would be are you making a false entry under 43.12 but the keyword is INTENTIONALLY. You are intentionally writing down a wrong number, but with an MX's properly worded entry I don't think the FSDO/FAA is gonna throw a fit. Logs are gone, gotta (re)start somewhere.
FWIW 43.12 seems to be getting an update as most online sources call it RESERVED and there is a NPRM from last year.