To stop early morning wakings, you cap naps, but you can also make the nap later. So you could move it later by 15 mins every three days or so (to give LO the chance to adjust). The idea is that the mornings after a while will follow the later times. It won't happen immediately but is worth persevering with.
I would say happy playing in the cot in the mornings is more likely to be an undertired WU rather than an OT baby, so this supports the idea of moving the nap later and possibly capping a nap too if that helps.
What about keeping a long morning nap (aiming for more than 1.5 hours so it's properly restorative. Then you could cap the pm nap if needed, which will help you get out and about more in the afternoons. If this suits you, then keep pushing that mornings nap later until you get a full nap of more than 1.5 hours.
As time passes you will be capping one nap eventually anyway to keep night time a reasonable length, and so BT doesn't get too late. This 2-1 nap transition can be tricky as each LO will come at it a different way, and it is a case of working out what is best for you, but do try and keep one of the naps longer than 1.5 hours and cap the other.
Have a look here for some more advice:
From 2 to 1 nap transition (10-12m and older)Don't be scared off by the average age of 10-12 months mentioned in the title, you're probably at the beginning of this rather than bear the nap dropping end, but worth a look anyway