I don't know where you are in England (or Scotland/Wales) but Exactrep has the reputation on-here for being the place to go to in the UK for VMax parts/work. Like any professional their prices aren't going to be cheap for a carburetor disassembly, cleaning and remounting, then the balancing, but you should be able to get a turn-key repair if nothing else is the matter.
my max is out of commission and has been for a few years
Before you do anything like taking the bike to someplace, get a powerful electric torch, I believe is the English term for a flashlight, and peer-into the gas tank. What do you see down-there? The gas tank should be shiny-bright on the inside bottom and the sides, if it isn't you need to evaluate what is causing it not-to-be. A rusted gas tank is useless, as your cleaned carbs will just become soon-obstructed, if you don't clean and evaluate the entire fuel system. The proper way to clean the gas tank is to remove it, remove the electrical reserve sending unit and install a blank-off plate, and then use some sort of a cleaning method to remove whatever is in-there.
Methods for accomplishing that run the gamut: ultrasonic tank, pressure-cleaning, high-% vinegar, called 'cleaning vinegar,' it comes in different concentrations, I would stay with something < 10%, my personal good results worked with 6%, which is much-higher than food-grade % concentrations. Moderately-numbered pH alkaline or acidic liquids will work, (Evaporust) but be-sure to do this with a face shield, a breathing mask, thick rubber gauntlet gloves rated for the type of chemical you're using. Electrolysis is another way proven to be successful in cleaning rusty tanks. Be aware that should you decide to initiate any of these methods, you need to understand PPE necessary to safeguard your skin, lungs, and eyes, and USE IT! There are many threads on-here about the individual methods described. Read-up on whatever method you think will work for you, get your PPE and it isn't a bad idea to have a charged water hose standing by, should you unfortunately have a chemical spill/splash, or other exposure.
Your use of youtube is another resource to use, based upon whatever method you may choose to initiate. Understand that anyone can post anything they want there, and you need to be skeptical and cautious about what you see/hear. If a preponderance of the youtube 'evidence' seems to-agree with what you've researched, don the PPE and have at-it. I will tell you that while filling your gas tank with Coca-Cola actually does have some rust-cutting results, dropping a handful of Mentos mints in-there won't make the Coca-Cola work any-better, but it will erupt in a spectacular mess.
Obviously, since you're cleaning the gas tank, you want to follow the fuel to the carbs, cleaning the rigid lines and rubber lines, along with checking for proper function of the gas pump, and an unobstructed fuel tank vent line. As everything is coming-apart in the fuel system, replace the fuel lines. You don't need a molded-horseshoe gas line off the gas tank as OEM has-it. You can use a ~9" 1/4" I.D. gas line hose, looped gently so as-to NOT KINK and run that to the gas filter, another item you can pick up a generic one approximately the same size from your local auto parts store, instead of spending whatever is the going rate in the UK for the OEM one. Here's they're about $21 USA for the OEM, a generic replacement should be about $7 here, so 1/3 the price. The one rubber hose I
would replace with the OEM, is the molded 'T' hose in the carburetor rack. It probably costs a bit more than the factory fuel filter, so buying the generic fuel filter and 'splurging' on the OEM fuel 'T' hose is a worthwhile compromise.
It sounds like you may-not have the knowledge to properly disassemble the carburetors, in which case, I think that you should entrust them to a shop like Exactrep. They would also (I hope!) ask you about the gas tank, if you were to bring them the carburetors off the bike, and to tell them, "It's been in-storage for several years." Remember that it's useless to clean the carburetors and neglect to clean the rest of the fuel delivery system.
A note on cleaning the fuel tank: should you undertake this yourself, once it's clean, you need to
immediately coat the gas tank interior with some-sort of oil product, because if you don't, it will flash-rust in a half-hour! I like to use a quart of cheap ATF. Empty it in, and turn the tank every which-way, to coat the interior. Of course, if the bike is immediately going back together, you can re-install it, but it should still get an oil coat, to prevent against the flash rust. Simply returning the gas tank to-service and filling it with fresh gas is the simplest, but remember that you need to give it a coat of oil until you dump in that gas. Oil the gas tank, remove the excess, and install it, re-fill the gas tank, and "Bob's yer uncle." The minimal amount of residual oil protecting the gas tank interior is not going to cause any spark plug fouling issues, if you let the tank drain of the oil you put in-there to protect against rust. Think of it as 'top-cylinder lubricant.'
A word on gas tank chemical liners: they work but you have-to
explicitly follow the directions! If you don't, the coating will make a cruddy-mess of your fuel delivery system, and you will have to solve that. There are probably businesses by where you are who can clean your gas tank, and coat it, compare that to the cost of a new gas tank. The last new VMax tank I bought was $200 and I had to wait a couple months to take delivery, now a recent price-check showed they're $300 USA, I don't know what the UK pricing is.
One of our members has a digital media available about doing a complete re-build of the engine, and one dealing with the carburetors. That would be a good place to-start. It's not expensive, and of-course it would pay for itself the first time you use it. His screen name is
Damon and he's from So. Lyon Michigan. PM him and inquire about the carb workshop media.