Early season is as likely to need spinning tackle as it is fly tackle!
I know a little about the Drowse, I’d say definitely a 13’ double hander needed early on especially if water is big, but unless you can get out somewhere to practice (or preferably a lesson) you may not be very effective with it initially. Spring salmon on the fly is hard going. The fishery may hire tackle?
Have a look for used tackle on adverts, done deal, or salmon fishing forum. You may be able to get some kit quite close to you. There’s lots of used salmon kit out there, the most important bit is matching the line to the rod.
I agree that Leeda magnums would make a good start, as would a JW young 1500 series Salmon size, if you don’t want to spend a lot. Ebay has lots of both for sale, £40 would get a useful version of either. If it’s not for you, you can probably resell at a similar cost.
If you go for a switch rod only, don’t go too light. Eg the Shakey oracle 7/8 is really a summer rod (fairly slow action too) and is closer to a Greys 6/7 Switch. The Shakespeare 8/9 is a better bet at the budget end. The online shop in enniskillen used to sell them as cheap as anyone and postage costs within Ireland are good. (I got a Used greys 7/8 for £100 on eBay, and it was spotless, so deals are out there).
Getting a reel for a switch is another thing, many trout reels too small, and salmon sizes unwieldy. you want the largest trout size ideally, I use 3 3/4” orvis Mid arbours, but you’d probably be OK with a vision Koma or another trout reel at the upper end of capacity, look for something that can take a WF8 + 150 of 30lb, although use gelspun if the switch line is tight. Dragonfly 100s or dragonfly 95 concepts can take a switch line too, fairly cheap on e bay and decent robust reels.
Btw, you’ve some really nice fly rivers not to far from you, the Owenea for one is something to think of targeting in the summer, where a switch or a longer single hander is perfect.