Can I make a 1hr full-transfer at Stansted?

I am flying frequently from/to London(Stansted) with Ryanair (~4 times a month since >1 year).

You should consider a transfer time of 60-120 min (without check-in luggage). Therefore, I strongly recommend to go for the second option. You may want to minimise the transfer times as follows:

Disembark the plane

My recommendation is to get a seat in one of the first rows of the plane. Even when both exit doors are used (not every time the case), the front door has an inbuilt gangway and leaving is quite fast. Thus, you avoid queuing behind all those people from your own plane.

Immigration

Stansted is not a maze and thus, you can quickly head to the immigration. Sometimes you will need to take a shuttle train (you cannot miss this either). In that case, remember to occupy a place close to the doors on the starboard (right) side of the train.

Stansted offers ePassport gates. In almost all cases, it was quicker to use them then the usual gates, even if the queues differ drastically.

There is a bus going to my town usually 5 minutes scheduled after my arrival. Due to the ePassport gates and since Ryanair usually arrives ahead schedule, I am able to reach the bus in 1 out of 6 times. Generally I leave immigration 5-25 minutes after disembarking the plane.

Security

To enter the next gate, you need to pass the security. It is mostly quick and convenient, but sometimes it can be just overcrowded. It took me already up to an hour, without any chances to optimize it.

To be on the safe side, you can book the FastTrack prior to your flight. You get more information on the linked page. In all other cases, you should expect 20-60 minutes for Stansted security.

Check-in

In case you are not aware that this is possible, you may want to check-in in advance to avoid administration time (and money) before your second flight.

Knowing Ryanair by reputation and having been on Stanstead several times, I would not dare to buy the early ticket, I might not even dare to buy the late ticket if it is essential that I make the second flight.

Ryanair does not do guarantied connections and they do also not guaranty any arrival time, they have very tight schedules and any problem with any airport anywhere in Europe can cause your incomming flight to be delayed as the plane was influenced by delays caused by other flights being delayed.

Under normal conditions, without passport check delays, you might be able to leave Stanstead within 20 minutes of your plane touching the tarmac, most airlines used to close check-in, when they still all had it, 30 minutes before the flight is due to leave at Stanstead.
Most recent flights I have had, from other airports I admit, boarding closed 30 minutes before the flight was due to leave.

If you add up, you see you can almost not make it between arrival and departure if you have to leave and re-enter the secure zone under the best of conditions and not at all with only 10 minutes delay in any of the parts.
Even when you can go from arriving to departure gate, without going through security, you will cut it really fine without any delay.

is it possible to exit the airport, and go through security again, and get to the gate within 55 minutes

It is possible, but is it likely? I would say it would be difficult for a person unaccustomed to the airport or one who arrived at it at a bad time. I would not recommend it.

Ryanair now offers a "business plus" fare which allows unlimited free changes on the day of departure. However it does not allow no shows, so you should book the later flight now and change to the earlier one at the airport. The service is £60, which depending how you value your time, may be a wise investment.

Today this morning I looked at this thread so thank you for the responses. Very helpful! However I would not recommend it as it was very stressful.

My flights today: Wroclaw at 7am > London Stanstead arriving 8.10am Then London Stanstead at 9.35am > Porto With check in luggage

Wroclaw > London Stanstead Departed 7am on time and it was due in London at 8.10. Western winds helped the plane go faster. Landed at 8.00. Actually disembarked the plane at 8.06. I was sitting in the aisle seat. I ran whilst following all the signs to "baggage". I then boarded a shuttle bus/train which took me to immigration/baggage and got off of the shuttle bus/train there. I ran again and went through security quite quickly. I watched the person in front of me who had an E Passport, how they placed their passport face down correctly, so I did the same. Luckily my luggage was already on the belt when I had exited immigration. I then ran to Ryanair self check in for luggage. I checked in my luggage. I knew I was tight on time so I had already purchased Fast Track for security. My queue was only 3 people long so I went through quickly. I then went through to WH Smith/Duty free shops. I saw on the board the gate to my next flight was to be displayed in 2 minutes. My gate was displayed at 8.35. I then had to go through loads of shops which took about 5 minutes, quickly walking. Then when I got to the "all gates" bit my gate was 10 minutes away. I walked slower than before this time as I knew I was near. I had priority boarding so I got to the queue at 8.52. No rush from there.

As I said before, I do not recommend such a short transfer/check in time with all the stress I suffered.

I assume you have to pass through immigration which also requires you to pass security again. Now I won't say yes or no but this sounds challenging at least to me:

1. you have to get off the plane: if you ever deboarded a Ryanair flight you know this might take a few minutes depending on your seat on the plane
2. walk to immigration/exit: walkways can be long and you might have to take a train I calculate at least 5-10 minutes
3. clear immigration: I queued for a good 15mins last time. If you have a machine-readable EU passport check if the wait at the automated gates is shorter.
4. walk from arrivals to security
5. clear security: you can save on time by paying a minor amount (3-5 pounds if I remember correctly) for fast lane security
6. run through the terminal to your flight. There is a long eating/shopping area the you can't cut and depending on your gate maybe even another train, calculate at least 10 minutes or 5 minutes running.

So you might be better off taking the 20h option especially since the loss of time is not that big. Or if money is not an issue, purchase both tickets. Finally if I understand correctly if you purchase your ticket through kiwi.com they have some kind of guaranty for missing this type of "connections".