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)
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)