Hello and welcome to BW forums
The first thing I notice in your EASY times is that his first A time is only 2hr 30 min. This is very short for a 7 month old. At this age we would expect to see at least 3hrs (guidance time for 6 months) and perhaps 3hr 15 or even longer for some. Here is a link to guidance times but you will see some get longer at this age, it is judged by how well your Lo sleeps and what suits the individual:
https://babywhispererforums.com/index.php?topic=84884.0I would probably start tomorrow with a 3hr first A time and see how that goes for a few days. Trying to put a baby to sleep when they are UT (under tired) is very hard work.
After that first nap though it is a bit difficult to see how long he is having awake. The times you have posted for his S time 10.30 - 12.00 is what you are aiming for rather than what happens. It really helps us here if you can record the times your LO sleeps and wakes. If he is only sleeping 30 mins what are you doing for the rest of that nap time?
The following nap time he may well be OT (over tired) by this point having had only a 30 min nap and followed by a 3hr 30 A time. Whilst 3hr 30 would be suitable for a lot of 7 month olds it would be more suitable after a good nap rather than a short nap.
Is there any reflux at all? Is he in discomfort/pain being laid on his back?
If not then you would need to persevere with adjusting how you settle him when you pick up.
the way I would imagine doing it would be to pick up to the shoulder (where he calms) and then slide him horizontally into arms. It would be helpful if he can become accustomed to calming in that laying down position to help you settle him in the cot. it is not something that will happen just in one day and he is likely going to be frustrated about it, you may need to bring him back to the shoulder to calm him and return to horizontal again several times.
When he is more comfortable with that you are likely to get a better result putting down in the cot and only briefly picking up.
Whilst doing this you can use shush/pat or if he doesn't like this you can do shush/rub or a key phrase repeated to reassure. key phrases are very handy during the sleep training process.
hope this helps