Welcome to HB Andy.
You have asked a few questions here and I will offer you my take on each of them. You have a classic vintage Pavoni and getting a replacement new one is not going to get you any material advantages. In actual fact, some of the parts on the newer machines are inferior to the oldies. For a fascinating look at the history of the pavonis and their parts, have a look at
http://www.francescoceccarelli.eu/lapavoni_pr_eng.htm - now there's a Pavoni enthusiast for you.
It sounds like to me that your thermostat might simply have some scale build which can be removed. I dont know how comfortable you are with diy, but another advantage of the Pavonis is their simplicity of design and therefore ease of repair in the rare occasions you need it. Have a look at this site which is as comprehensive as you can get when it comes to Pavoni repairs:
http://www.pavoniexpress.com/trouble.html, as well as this Forum, where there will be plenty of info on how to replace or fix a pressure stat. This might save you some cash, if your repair is indeed that costly (which being based in the UK myself, I can understand). Otherwise, a single repair after 20+ years of use is pretty exceptional, and perhaps another way looking at it.
Your other question on whether you should go for E61 semi HX or DB. There are indeed advantages to these machines over Pavoni's - the main ones being temperature management, which is the ability to pull back to back shots quickly in succession without overheating; steaming strength; ability to pull a shot and steam at the same time. Some would say ease of use and consistency of shot versus the levers, others would disagree. There are Pavoni advantages too - speed of warm up, portability, ability to properly preinfuse, reliability, cost.
However your main inquiry centred on whether your espresso will be "better" with an E61, then the that answer to that, IMO, is an emphatic "no". Different yes, better no. E61 machines automatically pump water at a constant rate at around 8-9 bar (adjustable). Pavonis machines rely on you as the pump, and you can vary this as you pull the shot, although you tend to find that the first to middle part of your pull is at the greatest pressure, then tailing off. This has an impact on the taste of the espresso. If you like loads of crema, booming chocolate notes with triple ristrettos packing in 20+ grams of coffee in a puck, then an E61 might be for you. However if you like a more delicately balanced coffee, nuanced and rounded with a little less crema - more like what you might find in Italy, then the advantages lie easily with the levers. It is a long winded way of say that it is very much down to personal preference, and of all the clear advantages an E61 might have over your Pavoni, better espresso isn't one of them. Far from it.
So I were you, I would get the old girl repaired, ideally by yourself if you can. Particularly if you only have a few shots per day as you say do. Pav Professionals were born for that purpose.
Now, for the most important advice.....
....a word on your coffee. I would urge you to stop using pre ground coffee - Lavazza, costa, Illy - whatever, and get yourself a high quality grinder as a priority. The grinders of the class you mention are very good, and with coffee from quality UK internet suppliers the like Square Mile, Londiunium Espresso, Has Bean, Monmouth, you will notice a huge improvement in taste using your current machine. Do this I can assure you will have a much more dramatic impact on your coffee than by buying a E61 machine in isolation.
So therefore, repaired Professional, new grinder, better coffee - and presto, you will be in espresso heaven.
Good luck!