Well, your questions have raised one for me:
Do your
lenses have optical stabilisation (OS mostly, but sometimes IS, for "image").
To continue, some camera bodies have IBIS, which sounds ornithological, but which
means "In-Body-Image-Stabilisation".
A part-answers to my own Q is: I don't think your camera body has IBIS. Anyway, if you
think that 1/250sec is still rather long for stationary birds, then some form of O/IS may
be needed.
Back to your questions:
For me, make it a "no" to an ideal
shutter speed...
For the compromise, it's also a non-definite answer. It's a decision you'll have to make.
That's what makes you a photographer. As you describe it, you're in the position to test
both situations. Whatever you come up with can be called your experience, and can be
shared here.
Just a recap: If your travels take you into serious wildlife territory, consider a "longer,
OS-capable
lens". In such an acquisition, get one that is full-frame capable. If you
eventually end up with an IBIS body, you can switch OFF the
lens OS.