Gotherington is one of the most expensive places in Cheltenham. Rentals are rare and house prices higher than they are in Charlton Kings.
If you want to guarantee a place at a school and are willing to be dishonest, then go regularly to the church attached to Christchurch, or Leckhampton CoE. We personally decided against that, because I wasn't comfortable with the idea, but you jump the queue ahead of parents who live locally. Christchurch is particularly known for this - families living one tenth of a mile away fail to get placed, because people go regularly to church for the 2 years prior to applying and then queuejump accordingly. You can live anywhere in town, but get in if the vicar says you are a regular attender, and the next-door neighbour of a house we looked at in Queen's Retreat (if you look on Google, it's just 2 streets away) said her kids didn't get in. Christchurch has the advantage that they get to use Cheltenham Ladies College's facilities, too, as part of their charitable status ("helping the local community"). I get the feeling that's reasonably near to you, no? As both schools in Special Measures aren't a million miles away.
You could buy in a cheaper area, then rent a place close to a good school for a year that covers application dates and the first term. As long as you genuinely live there (some people rent places and keep them empty just for the address - which is fraud) you'd get a place.
It's painful and I sympathise. We just got a house in Charlton Kings which we can barely afford and is light years less nice than what the money would get us in Landsdown, where we'd rather be and have been the past few years. But we aren't close enough to the good local schools, and won't fake the church attendance, so we'd be allocated a school we don't want otherwise. And an additional note of warning - people at CKIS who live just under half a mile away failed to get in last year, and they know there is a big bulge in pre-school population ahead. Our place is a tenth of a mile - it's more or less on the school's street - because we didn't want to spend all that money, only to find we weren't near enough anyway. And estate agents lie through their teeth on the subject. I had several insist that a house a mile away would be just fine, and they knew that for a fact because of XYZ. But the other positive there is that both Glenfall and Warden Hill are really good schools as well, and you stand a shot at both, as they are fully subscribed, but only just.
Basically you need to do your homework on each school - the number of kids applying as first choice options tells you how likely you are to get yours in. Church schools usually allow local church attender's kids first dibs, so if you aren't one and the school is very good, you have little chance of your child going. Non-church excellent schools such as Charlton Kings and Gotherington are in expensive areas and you need to live almost next door. Sad, but true.