I do not recommend modifying any Amateur radio for use on 11m, but if you intend to get your ticket and play on the adult bands my opinion is GET THE 710!!!!!! I think the 710 and the 7300 are very close to each other in TX performance and bells and whistles, but the 710 is head and shoulders above any Icom offering in Receive quality. The several filtering modes and Digital Noise Reduction are superior and easily adjusted to varying conditions. I've worked a few dozen weak-signal SSB DX contacts on the HF bands that I could not hear on other radios. It's the first Yaesu I've owned but I'm hooked and won't be going back to other brands.
You mentioned liking the idea of the external monitor, but one word of caution if you choose the 710: be certain the monitor you buy is DVI capable. Connecting other monitor types can/has caused issues with some 710s, up to and including letting some Magic Smoke out of the radio. I bought a small, inexpensive DVI monitor and cable and have had zero issues.
Hope you get your Amateur ticket, if you like DXing you'll really enjoy talking thousands of miles with 100w on the upper HF bands.
73 and good luck.