I agree that if you've built up a £600 credit, then you were probably paying too much for your old tariff, so if your current tariff is twice as expensive as your old one, you probably don't need to double your monthly payment, but you might be happy to leave it as it is rather than try and convince BG to lower your DD.
However, MSE is your friend here.
Your bill should give you annual usage figures, so use the calculator to check what your DD should be:
https://www.moneysavingexpert.com/utilities/lower-energy-direct-debits/
If it's too high, you could call them and say you've used the MSE calculator to work out what your DD should be and you'd like to pay that amount.
MSE are also advising people to ask for any credit back now, as this is the time of year when you'll be at zero, as you'll build up credit to go towards your winter bills.
As for what prices are going to do, if you've come off a fix, chances are you're on the standard price guarantee tariff. This is related to the market price and is subsidised by the government. It automatically changes each quarter, so is expected to go down at the beginning of July. There aren't really any new fixes that are cheaper than this.
As for whether or not it's worth changing, you might decide to stay where you are. Or you might decide to switch for better customer service, or an easier online experience. I'm with Octopus, and I think they're great. You can do a lot of things online yourself and they're very transparent and fair with DD amounts. We've made quite a lot of changes to cut our gas usage and I was able to just click in my online account to get the excess credit back.
If you're interested in switching, if you use my referral link, we each get £50 credit (or you could stay where you are, or just sign up yourself without the referral if you prefer)
https://share.octopus.energy/loved-moon-894