A Bav 34 is pretty good for what you want to do - the limitation will be you not the boat. Plenty big enough for singlehanding or 2 up (30 years ago would have been considered the height of luxury!).
Your seems to be very well setup already. For coastal (and offshore in the sense of going cross channel, down the Atlantic coast etc) you have more than enough battery and charging capacity already - you have more than double the standard. You only need to think about increasing if you want to spend more time at anchor and be independent of the land. Spend some time and money reducing consumption - LEDs, extra fridge insulation are good starts. Same with water capacity. Typical water usage for drinking/eating/cooking is between 5-10l a day. The big consumer is showers. Typical round Britain and even long term coastal sailing is really a series of day sails with the odd overnight and anywhere between 30-50% under motor. Not sure why you want to increase stowage. A 2 cabin has more than enough for one or 2 people. It might become a problem if you are wanting to provision for 20 days offshore but for what you describe you are never going to be away from shore for more than a few days. Worth reading some of the books and accounts of round Britain to get an idea of how other people manage. For example my sailmaker went round with his wife (and dog) in a Contessa 27 very comfortably in just over 3 months, but others take it slowly over a season or 2. There are almost as may ways of doing it as there are people who do it!
Agree, absolutely no need to drop the keel unless there are clear signs of failure of the keel/hull joint. Equally why do you think you need a survey? For navigation, get a good chartplotter and AIS, mounted at the helm with a backup of a phone or a tablet (and paper charts!). Good autopilot, preferably below decks type rather than wheel. 4 man liferaft and an EPIRB. Get an assessment of your current sails. Talk to a sailmaker for advice, perhaps looking at an upgraded main and jib, probably a bit smaller than the standard and an offwind sail such as cruising chute. For singlehanding the key is simplicity of handling rather than performance. Personally I would not spend that sort of money (could be £8k+) until I had some experience of offshore sailing. The way you describe it your boat is already better set up than the vast majority of similar size and age boats!
Don't be seduced by old heavy "offshore" boats. The sort that you could buy for similar money will be old, knackered, cramped, slow, and nowhere as near well put together as you imagine.
Hope this helps
it is common advice when undertaking the sort of sailing you are planning is to go with the boat you have and know