I actually came from the exact same Canon DSLR progression 1D3 to 5D3 + 7D2, then adding the OM-D E-M1 II. I’m constantly amazed at how well it performs.
Sure the DOF isn’t crazy shallow like full frame, but you certainly can achieve shallow DOF and subject separation for a similar look. Honestly, I’ve had more issues with slightly missing focus and having too shallow DOF in the past on FF with lenses like the 85L II and 50 1.4, so a little more isn’t always a bad thing for me. It lacks a bit in sports shooting in terms of subject tracking, but it’s no slouch... especially considering it’s only a 2nd gen product. They’ve already improved it with firmware updates and I’m sure they’ll continue to do so. Part of that is also inexperience with the system on my part I’m sure, since I’m much more used to shooting my 5D3/7D2 with good glass (70-200 II, 300 2.8 IS). Unfortunately the 40-150 2.8 PRO won’t give you the same separation as the EF 300 2.8 IS, but it does give you the same field of view and takes the Oly 1.4x TC extremely well. Battery life on the EM1 II is a non-issue since they went to the bigger battery. It lasts a long time now. It is an issue with the older/smaller batteries like in my wife’s EM10 II, so we have plenty of spares for her camera.
I actually used the EM1 II for my first paid shoot just last week after getting used to it for about 6 months. It’s convinced me that mirrorless is the future since it’s so much more advanced than my Canon DSLR’s at this point. I shot softball individial/team pics outdoors at 11am, which means blazing sun. The back LCD was nearly impossible to read and I needed to see the review photo clearly since I was using strobes. The EM1 II handled it amazingly well, with face detect nailing the focus on their faces every time and the ability to review the photo in the EVF made it super quick and easy to make adjustments and get some nice shots of the girls.