Ted,
Stephan gives some great comments on all three radios.
As for the 847 on HF, I think there is a audio clip on the internet comparing the 847 and TenTec Corsair II receivers. I have both of these rigs and the difference is very clear. Listening to my 847 on HF is not a pleasurable experience as the receiver is very noisy. For this reason, my old Corsair II does all HF work at least until I get a new HF rig. Eham reviews on the Corsair attest to its great receiver.
As for satellite operations, the 847 is a tough and a great rig. Mine has been running since the beginnings of AO-40 with no problems. It has some engineering mistakes like the AF gain not being linear along with other quirks but I've gotten my investment back many times over.
If you've got the cash, I would read the QST review on the 9100 and make an executive decision.
GL
Mike (K9QHO)