Looking at the satellite view, both peaks appear to have some pretty good rock climbing at the top. Especially the south (red) peak.
Also, I just looked up the land ownership, and the west side is BLM. Both peaks and the north/east/south are State Trust Land (I'm sure you have your permit

). There's a parcel of private land to the south, which I believe is that spur road you mention as leading to a shorter trip (and a few mines on the topo map). It may or may not be gated. Big Reef Mill area to the northeast (and that road) are not private.
If the road into Trilogy Wash on the west side is a decent road, it might be easier to ascend from that side somewhere.
The State Trust land is on a grazing lease, so you might encounter some very unhappy cows? (unhappy cause there isn't a whole lot of delicious green grass to graze in the area).