Isn't everyone overthinking this launch sequence. Military aircraft designers solved this long ago by using a sliding rail to avoid rockets hitting the wings that they are mounted on. Why not use one for LOHAN?
I like KISS for this part of the design. Flying the thing later will be hard enough.
To get a vertical attitude from a rising baloon you can hang a weight beneath the main payload container - that'll be Vulture2. But you don't connect it directly to the payload container.
You have it slot onto a rail that is suspended at a 45 degree up angle and connected to the main payload container.
Use either low powered RF, or IR or old fasioned contact points to have the main payload communicate with Vulture 2 and get it to trigger Vulture2 to fire and fly it straight off the rail.
The rail will need to be sufficiently rigid to withstand the initial tug of the rocket firing, so its hanging on a rigid lightweight structure not on a rope. But we're talking a few grams of structure not kilos of the thing hanging there.
As for the Vulture 2 itself: Some missiles used to have rail mounts designed into the external structure, others had sprung trips to either discard the mount or to have it retract inside the body as the mount cleared the rail end.
Since it doesn't exist yet either approach could be used with Vulture 2.