You can always 'fib' and imply to your priest that you ARE putting the catholic school first (and need his reference for this) but that you want to ensure that if they don't get in, that they at least get a Christian education, so you are putting the CofE school second, and hence need a reference for that one too. What order you then actually put them in is strictly none of his business!
Furthermore, you probably don't need a 'reference' as such, but simply need the priest to sign a form stating how often you attend church (and since when). He can't really object to that. However if you do change to a different church, you might find you still need first priest's signature, as the school might want to have proof that you have been a regular church goer for more than the time that you will have been going to the new church.
When we had our forms signed, we actually presented the deacon with 3 forms from 3 different schools, only one of which was catholic, the other two CofE. Whereas others I know brought forms from 4 different catholic schools, spread wide and far, with zero chance of them getting in anyway (because of the distance). All they are doing is risking that they won't get into any of their choices and are thus allocated a random school.
As to the second part of your question, how big is the chance of getting in? There really is no point in guessing, and asking on MN won't really help you much, as the situation is different with every school.
You can however ask the school for a break-down of admissions in the last year(s) - how many children applied, and were admitted under, which category. Sometimes schools even list this info in their admissions leaflet, sometimes however you have to ask them for it separately. It should look a bit like this (for eg. an intake of 30):
Looked after children: 2 applied, 2 admitted
CofE children: 17 applied, 17 admitted
Other Christian denominations: 18 applied, 11 admitted, furthest distance 0.7km
Any other children, 21 applied, 0 admitted.
In which case you would have good chances, given that you live nearby.
Or it could look like this:
Looked after children: 2 applied, 2 admitted
CofE children: 44 applied, 28 admitted, furthest distance 0.8km
Other Christians: 22 applied, 0 admitted
Any other children: 12 applied, 0 admitted
In which case your chances would be very small and would depend on a massive change of circumstances (bulge year, recent downgrade from outstanding to special measures, …)
Or it could look like this:
LAC: 2 appl. 2 adm.
CofE children: 12 appl. 12 adm.
Other Christians: 7 appl. 7 adm.
Any other children: 14 appl. 9 adm. furthest distance 2.1km
In which case you would be nearly certain to get a place and could even risk applying without your priest's reference.
My point is, without knowing this, it is really nothing but guesswork, based on nothing factual.