I guess it depends on whether you consider the whole process to be a bit Heath Robinson or not.

It's your time and money so who's to say, especially as it doesn't seem like you're prioritising sound quality?

Even if your LPs could be considered as new you'd still be stuck with a pretty lousy product: AudibleOddities – Audio Mastering Engineer for Internet, CD, and Vinyl | Vinyl

That said, CDs and FLAC files could, and regularly do, fail just as dramatically.

However I doubt very much if an analogue versus digital discussion is going to help, as it really does sound like only a soldering iron will scratch that itch.

Personally I'd be wary of chucking too much dosh at this project, but that's just me. You know, no matter how enjoyable the process, you will ultimately end up with pretty naff media.