I'd get a .300 RUM over a 7mm RUM if you did. That's alotta powder to burn, even in a 26" barrel, and the .308" dia would do it better/more efficiently.
Get the sendero if you're gonna get a RUM.

If you want a lighter rifle, get a smaller round in something lighter... maybe a .270wsm if you want something flat shooting, and a small bore.
I think you should keep this RUM to use on the bigger stuff, not antelope and coyotes.

Is this going to be your one and only rifle? I can understand having a truly ultra mag if I already had something smaller, but you say you can't afford different rifles, if that's the case I'd strongly suggest more of an all around. Also a legacy rifle...I don't think you want your 7mm RUM to go the way of the .264 win mag legacy rifles...which I think it very well could. How popular is the .300 RUM even?

How about a .270wsm, .300wsm, 7mm rem mag, .300wby?