cuisto,
The backstay is a non-issue. No problem with leaving it loose during the lift.
And, your mast will be stable and
sorta' safe by raising it with only the forestay and the babystays ... to a point. As Rick mentioned above, the mast will want to rest solidly on its maststep (tabernacle??). However, this should be a one-time deal, not a regular process. Babystays are rarely taut enough to fully stabilize the mast. As Tangent wrote above, the slightest wind-on-beam will want to push your mast off to one side of the boat. I just hope your babystays are "close to" fully taut. The problem is, you can't really determine how taut they'll be with the mast down.
Raising the mast 'sans shrouds' would become an ordeal (each time) as a regular procedure. But the real reason is ... it's not really a safe or logical process to "shroud" the mast after it is fully erect. In fact, it's virtually impossible to do so safely. Here's why.
The "conflict" among the forestay and the four shrouds provides the triangulating force to stabilize the mast. The contradictory "tension" among three points, foretang and chainplates, represents a physical "tripod" that safely "stands" the mast. It won't be possible to attach the four shrouds without tipping the mast aftwards by 10 to 15 degrees, since the shrouds should be going into
serious tension (300+ lbs.) during the lift from ~75 degrees to 88 degrees-erect.
I cannot imagine any combination of mods that would require your approach. But then, I'm not lookin' at it~!
It won't hit your truck, but it easily could fall to either side. Best of luck~!
