I wonder if a significant portion of the difference you're hearing and feeling is more in the amplification and less in the profile?
For the powered Kemper, you're using it's built-in solid state amplifier. For the tube amp, you're using it's power amp.
Maybe try testing your Kemper line-out feeding into the "return" of the fx loop of your tube amp if it has one, bypassing the preamp and EQ on your amp and going straight into the amp's tube power amp and see if that gets you closer to what you hear from your tube amp?
That would eliminate the difference between Kemper's on-board solid state amp and your tube amp's power amp.
Yes... Already tried this in the past numerous times.
It (Kemper SS power amplifier section) is a large part of the issue.
However, you have to be careful as the "DI profile" already has the tube poweramp in it, so when you add a tube power amp to a profile, you are in effect, doubling up on the power amp section.
But all that aside, yes, a large group of members here have found that the SS poweramp is a huge issue that is not allowing a DI profile to sound, feel or react like the original reference amp, when played thru a 4X12 (or any cab...).
However, I do realize this was NOT the main reason that the Kemper was built. The Kemper performs amazing thru any PA system and is a real pleasure to use... just using the power section thru cabs is still a struggle.