Phase Cancelation Between Gain Stages - Seeking Advice

After reading, I realized I was a bit confused. It sounded like you were having phase issues between amp and DI signals, but upon reading again, it seems like you're just taking a DI? If so, phase shouldn't come into play here. It sounds like you just want the mids that a mic'd cab will give you.

And as far as the DI not sounding like the amp, that's completely normal. I would suggest duplicating your DI track and putting some sort of amp simulator plugin on there. Lots of affordable options out there. I typically cut all of the highs out of my DI track and compress the hell out of it for clean, consistent low end. Then I use the "amp" track for mids and character (and cut the lows out of that)
 
I did exactly this for a recent live recording my band was having pro shot. Tracked the bass DI as a fail safe/for potential blending, Shure mic on the cabinet (can't remember which, it was a kick drum mic) for FOH use and any overdrive and effects.

After messing around with DI and plugins for "amp" sounds for recording, this was immediately more satisfying than any method I'd used before. The band got a little surgical with the EQ, but honestly just some low passing and cursory blending of the two signals was satisfactory to me.

This is what I do. We take a DI straight out of the bass, direct to the board. Then we'll take the parallel out from the DI and run it through my normal board and amp, into the studio's cab. SM7B on one speaker, RE20 on another.
 
If the Mic sounds good - use the Mic. With good Mic choice & proper placement you should be able to get a great tone.

Secondly - simplify the pedalboard for each song. I.E. Only have the pedals you use for each song on the board, swap them in and out as you go.
This approach was a firm demand from one of the engineers I recorded with some years ago, not debating, not negotiating!

FWIW - sometimes a pedal will flip the polarity. I sometimes found that pedal needed to be sold as I couldn't get it to gel with my pedalboard, other times it just needed to be AFTER a certain other effect. Good Luck