To my surprise, not only will the F6000-series rigs operate on FM, they also allow all necessary parameters to be configured to allow operation via 10m repeaters.
As soon as FM is selected as the mode, a menu opens that allows setting the desired offset, offset direction, squelch level and CTCSS tone frequency.
Repeaters on 10m use a -100 kHz offset and usually operate on input frequencies (rx freq for you/me, the users) of:
Unfortunately, I was not able to key up any repeaters on any of those frequencies. That may be due to poor propagation at the moment or because 10m repeater operators have discontinued the use of their repeaters due to inactivity.
One of my most bizarre QSO's ever (25 years ago) was working a French station from my QTH in Connecticut, via a 10m FM repeater in Argentina.
Repeaters aside, the 10m FM simplex calling frequency is 29.600 MHz.
I'll monitor those frequencies from time to time and report here if any activity is sighted.