We rode to Monte Cristo on gravel bikes as part of a climb up a nearby peak. We left on the "alternate" route, per the recommendation by a previous poster in 2021. We disagreed with this recommendation, so wanted to provide a different perspective and an update on conditions.
The road is sufficiently overgrown at this point that it is more like singletrack. This was not an issue, just something to note. There were also a number of logs that we had to get off our bikes for either to go under or around. Some had cutouts but the cutouts were too narrow for us to ride through. (YMMV) Some of the climbs were also quite chunky in addition to being steep. In general, there was more hike a bike than we were expecting and we didn't particularly enjoy it, so we tried the other route back and much preferred it. The "road" sections are actually gravel road you can ride two abreast, and in general we felt like we walked less. The river crossing was no big deal (in late August). We did ride out at 5:30pm on a Friday so were not really contending with hikers.