Hello and welcome to BW forums
It looks like you've made a good start with shush/pat
I think the thing to bare in mind is that when you are implementing a new routine or a new method of soothing for sleep some disturbance is to be expected. Having a few nights which are different to the norm may just be part of your LO adjusting to the new routine you are introducing and doesn't mean there is going to be a long term problem at night. In the long term it would be expected that learning to self sooth to sleep would help both the day and night sleep.
With regards to sleeping on her side, it is fine to adapt the shush/pat if you would like your baby to sleep on her back. I always slept mine on his back and many people on the forums have adapted shush/pat to what suits them and their baby. Some people pat on on baby's back until drowsy (or asleep in those early days of sleep training) and then gently move LO to her back continuing to use a firm hand or a pat on her front/nappy area/hip. Some people prefer to put down on the back right away and do patting on the front/hip, the patting doesn't need to be hard or cause any discomfort. Mine did better with a rub/slight rock as patting seemed to make his reflux worse, this is also fine and the slight rocking motion can be weaned in the same way at patting by reducing reducing until LO learns to sleep alone.
Looking at your EASY the early evening NWs might have been due to a little OT (overtired) as the last A time is a bit longer at 1hr 45, this may also be a reason it took longer to settle her if she was a touch OT. I notice earlier in the day when it took 30 mins to settle her to sleep it had also been a long A time of 2hrs. Sometimes during sleep training the A times do get a bit long as LO is being shush/patted rather than held or in the car/pram and may find it harder to get to sleep. You might try a shorter A time and see if settling is easier - but in any case 30 mins does not sound unusual for a LO being taught the early stages of self soothing and independent sleep. It should get easier with consistency and as your LO learns she is safe and fine to fall asleep being patted...and then without being patted
I would say that with older children to care for it is well worth doing as you are and having some of those nap times in the pram/car and some at home. If you can keep the routine regular each day (eg first nap always in pram, second nap always in moses/cot etc) you are likely to see quicker results or find the whole routine goes more smoothly.
Keep in mind that there are many growth spurts at this young age too - extra night waking may might look like it is because of a new routine but could be due to hunger through a GS.
Are you putting the moses basket on an incline to help with the reflux? Often prams and car seats are more comfortable for refluxers because they are slightly more upright in them so the acid stays down. I believe there may be aids to fit moses baskets such as wedges and blocks which might be worth looking into.
Looks like a great start even if it doesn't feel it right now - after all it looks like she was sleeping in her moses basket from 7.30pm until morning even if you did need to resettle her
