Andrew, I have challenging vocals to record, so can relate. I admire vocalists who can record in a single take. That ain't me though.

Don't see anything you're doing WRONG, but whether what you're doing what you describe RIGHT depends on context and what you hear, or want to hear. So like everything else...it depends!

Yes, definitely re-record vocals that don't meet your goals. Practice using voice control to level your vocal levels and minimize plosives, clicks and other non-musical sounds. This works better than processing!

Compression is good in moderation, but I use gain staging (adjusting the volume) just as much when I want to balance the levels in a particular passage. I do find a gentle compression peaking at 3 dB of Gain Reduction can be helpful and (usually) transparent. All compressors aren't equal though, so find one that pleases your ears.

Adding EQ "presence" at around 3k can make your vocals cut through the mix. I like the concept of triple tracking, but rarely use it. The Beatles did pretty good with double tracking, right? The main problem with double or triple tracking is it doesn't suit all music styles. Great for rock, not so great for jazz.

My main vocal FX for rock/pop are tape delay with a smidge of plate reverb. The delay and/or reverb can be panned if you like. I'll sometimes combine this with a doubled vocal panned opposite the delay. It's then SORT of triple tracking though, isn't it? Still a better rock sound than jazz. For jazz and standards I'll skip the delay and double tracking.

Don't have any YouTube videos to recommend, though I've watched hundreds by now. I'd just recommend that you (1) work on vocal technique, (2) listen critically to what you hear, (3) keep the ideas that work for your taste, (4) discard the rest of the ideas (even mine!). My experience is that your results WILL improve with practice. I've recorded 1000+ song vocals, so if practice made perfect, I would be...but I'm definitely NOT!

Happy singing!!

DC Ron
BiaB Audiophile
Presonus Studio One
StudioCat DAW dual screen
Presonus Faderport 16
Too many guitars (is that a thing?)