Panasonic lenses with IS do not disable or limit IBIS on the E-M1 II. Rather, the user must choose between IBIS and lens OIS, and the IBIS in that body is far more effective than the OIS of any Panasonic lens.
It's true that combined IS can be even better, but only if the body already has very good IBIS. A Panasonic GX9 using dual-IS with the 100-300 II is less stable than an E-M1 II with that lens and IBIS alone. Given OP's budget, the only option for combined IS that actually outperforms the E-M1 II IBIS is a Panasonic G9 with the 100-300, and the G9 does not have phase-detect autofocus.
I found trying to rely on Panasonic's depth from defocus technology for birds disappointing.
