Hi again
Sounds like you are doing well, especially working out that he prefers to stay in the cot unless he is crying hard, having a hand on him is fine, it is also fine to shush/pat in the cot too (or just pat or a stroke/rub) if that helps him to calm down and relax.
4 months is a time when many babies short nap so it can be a tricky time to start sleep training because there is a developmental period where these short naps are common even for babies who have already learned to sleep independently. The developmental period usually passes by around 6 months which should give you hope, although that month ahead can feel much longer when you're in the thick of it.
It may be possible for you to help him stay asleep using W2S (wake to sleep) here is a link describing it, have a look at naps option 1
https://babywhispererforums.com/index.php?topic=223809.0it is often easier to do this and catch LO before they wake or as they wake and begin the soothing before they get themselves fully alert and into the crying. Once they are crying it can take a lot more time and effort to get them to relax and sleep again. This can cut down on the work load and increase the sleep time. It is also a method used to teach your LO that he is supposed to sleep longer and can help him to learn to transition from one sleep cycle to the next on his own. You would usually do this W2S for 3 days, hold off day 4 to see what happens and then begin another cycle if he fully woke. You can continue in these cycles.
Another thing is to check his routine is suitable for him as a routine which is not appropriate for his age or individual needs will make it much harder for him to sleep or stay asleep, and therefore harder for you to get him back off to sleep.
If you would like to post your EAS times I can have a look?
Do I continue doing what I am doing now and stick to the plan? If he wakes up early try PU/PD for the rest of the nap time?
This is the approach used by Tracy, yes. Many parents find this too much work though so if you feel lacking in energy or losing patience then it is probably better to limit how long you try to resettle for (ie if it doesn't look like he is calming within 10 mins you might give up then) or to choose one nap per day where you put in that level of effort to resettle (this helps towards the sleep training) and let the other naps go. If you choose this second option I suggest you stick with the same nap every day as LOs pick up habits (eg nap 1).
Also, should I move the routine if he wakes up at before 7?
Again there are two options really. One is to treat all wake ups prior to 7am as NWs (night waking) and keep him in his room with your support if he is crying to try to resettle him - this teaches him when morning starts.The other is to accept that he wakes early, start the day but adapt the routine to be suitable (counting the first A from when he wakes). If the WU time is a problem for you then you'd need to look at the overall routine to see what needs to change to encourage a suitable WU time.
Please feel free to ask further questions and to post your EAS times if you have them. If not you can begin recording them and post in a few days. When you post times it helps us a great deal if you post the real times of what actually happened rather than the times you hope for or a routine you would like to see, although obviously it's ok to say you'd prefer a later morning wake up time or if you need naps to fit in with some non-movable family commitment or something of that nature.
hope this helps some