Changing planes in EWR with a non connecting flight - Can i do it in 3.5 hours?

Given the substantial savings, if you have the time do an overnight at one of the airport hotels. Much less stressful. If your TAP flight is on time you probably have enough time to get into NY for a nice dinner. Head back home the next day.

Is there a later flight that would give you a bit more time?

I have been to EWR only on domestic flights and was pleasantly surprised by the relative efficiency. No idea how immigration might work.

With the amount of savings you are looking at, it is certainly feasible to spend some of it on a hotel and fly the next day and not be stuck buying a new air ticket to get home in case your 1st flight is delayed or long lines do you in.

The other option is to do carry on only and eliminate the baggage claim and re-check process.

I'd do it, without the hotel. Just be prepared to pay for a last-minute flight the next day or something if you miss your original flight home. It's a risk for sure. But booking the hotel just guarantees you have to pay extra and get home a day later. If you hate risk, just book the hotel and fly on the next day.

This is why I like having Southwest Airlines points: I can book award flights that can be canceled at the last minute for free. So if I were doing this trip, I'd book a Southwest flight the same day and one the next day and just cancel the second one if I don't need it.

Consider downsizing what you pack so you can do all carry-ons and maybe save a little time connecting if you have a tight connection. I started doing that a few years ago when going to Europe and don't miss the big bags I used to check.

Global Entry might save you some time: you'd breeze through immigration when returning to the US plus also have TSA-Precheck when going back through security in Newark.

Like all things, there is some risk. With average schedules, min of delay, you should be OK -- BUT -- the operative word is -- should be. There are no guarantees. Having Global Entry would be helpful. Customs isn't an issue but immigration can be. I just came back from South America via Miami with a similar decision. Landed in Miami at 4.30 am. Should I take a 7am flight or the 11am. Finally opted for the 11am flight but could have made the 7am easily. Did have a nice leisurely breakfast.

I have made connections of a similar timing BUT...I never check a bag. There have been several times where I would not have made the connection if I had to go to baggage claim ,wait for bags to unload and collect bag.
I do other things to improve my chances, getting a seat near the front of the plane, ideally business class or premium economy which is typically behind business class. And of course, you have checked into the non connecting flight and you have the boarding pass.
Getting in front, walking briskly, and most important not waiting for a checked bag, puts you in front of the rest of the herd.
Also TSA precheck if you have it ( and I would highly recommend this) will also save a little to a lot of time going through security.

As Harry asks: You've gotta ask yourself one question: "Do I feel lucky?"