2om30 has most of the basic ideas printed out. By hooking your right leg(as per the illustration you posted) and sitting up, you could move into an omoplata-style shoulder lock. If you get your arms closer up towards the tricep, you could perform a fairly unstable(amateur-catcher only) armlock by pinning the hand to your chest and 'pulling' the tricep while arching your back, instead of raising your hips, to put some tension on the elbow and possibly get the tap.
If you're good on your transition skills, you could switch over to some standard armbars from there. The first you would need to be most careful with, but make sure you have the arm secured, and mostly just 'roll over' the arm, and you'd be set to move your right leg across the face, pull your body over, and you'd be face down, matching your partner, for a standard armbar. If you're face down, you have a harder time controlling your force and weight distribution though, so make sure you don't slip and lose balance or press too hard against the elbow joint, as you're laying on top of it, rather than underneath it this way..
A little bit more technically difficult would be to catch the arm by hooking your right leg, sit up into an omoplata, then push up, rotate, and land on the OPPOSITE side of your opponent. With a 180 degree rotation, you'll land on your back, and your opponent will be laying on their back, ready for the textbook armbar. This one would be rather difficult for a beginner, but with a bit of practice, should perfectly solve your problem, especially if this is something you end up doing on a regular basis, like you said. This illustration is a bit more... Difficult to understand? I'm not too good at MSpaint.
The second one you'll want to take slow until you get better as well. There's some risk, if you move too fast, of accidentally pulling and really cranking an omoplata. If you do get the omoplata, or are good with that lock to begin with, this would be the best solution. Otherwise, if you're still working on transitional experience and standard locks, hopefully this one can help you out.
First image is the roll-over to armlock, Second image is the omoplata and spin.