I recently acquired one of my "all-time want" guns as a guy growing up in the '80's; an original Action Arms imported IMI Uzi Model B carbines.  This is the first firearm that I have truly wanted to SBR instead of just waiting around for them to do away with NFA items.  Is there anything I need to know to help things along (speed-up) or assure myself all bases are covered and done right before submitting?  I've seen some  people talk about engraving the under side of the barrel but that didn't sound right to me, as I thought it had to be on the receiver.  Would maybe under the folding stock be a good place?  It would be really nice if I could just do the barrel, incase I wanted to sell it later on but I highly doubt I would anyway.  Any help and/or advice will be very appreciated.

I think I have found probably all the information I need above in the stickies but if there is any input directly referring to Uzi's I'd still appreciate any info.

Since over a year ago, all newly registered NFA has to have the registrant's name and place of manufacture engraved on the receiver. (The caliber marking can still be on the barrel.)

Sure.
Just know the word "conspicuously" appears in the CFR describing/requiring the engraving, which is 27 CFR 479.102 Identification of firearms.
This is a really common thing to do though.

It would not be in compliance with the latest edition of the CFR.

Does anyone ever really look for these things? Highly unlikely.
Would you be charged with an NFA violation if ATF found out? Even less likely.

What you can still do is buy someone's existing UZI SBR that doesn't have any engraving on the receiver.
Even if it was registered after the recent change to CFR regarding receiver engraving, only the maker is required to engrave. (So if you didn't make it you cannot be held accountable to the engraving standard.)

I'll save you a potential headache specific to the Uzi carbines. Make sure to list the model as "UZI B" on your form 1, lots of people put just "UZI" and get denied.

And don’t put Action Arms as the manufacturer. It’s IMI, Israel.

Both of my are laser engraved under receiver where the folder folds up. A little birchwood casey super blue fades it nice. I look at it this way, we have all had to stare at some of our guns with the
stupid "please read instruction manual before using" for years. John Smith Austin Tx on a gun wouldn't bother me a bit.

I engraved the barrel on mine for the same reason you mentioned but this was also a few years ago..im not up to speed on current CFR, albeit so long as I have the approved paperwork, I'm not worried about engraving either even though all of my stuff is in compliance, the engraving isn't even on my mind if I were to not do it for a few months or at all..

maybe keep the original barrel and buy one pre threaded in case you need to sell without forms.