Kings is 60% at CE at moment.
Both schools very similar apart from co-ed bit, and Tonbridge has marginally better reputation for SEN (neither shine particularly brightly in that area IMO). I think Kings has fallen down a bit in terms of Rugby in the last couple of years, but is ahead in (boys) hockey. The relatively new head is IMO slightly bonkers but is very involved with the school and teaches all the shells in one lesson or another. I know the housemasters of three of the houses at King's and can vouch that they are very pastoral. I'm not sure i agree that kings is mostly full boarding - I think its more like 50-50. Over 1/3 of school are from local area (feeding in from Wellesley and JKS) so nearly all of these will be weekly/day.
If Tonbridge doesn't work out then Kings would be fine. As for better? Well depends on yardstick. You will be more blown away by the architecture I think - the whole school is within the World Heritage Site (one of the main dining rooms is where the four and twenty blackbirds came out of the pie). The boarding accommodation is same quality I think as Tonbridge (although I've only visited one Tonbridge house). But Tonbridge is more 'contained' whereas the kings kids are forever back and forth because sports facilities are 2/3 mile away, and library is a few hundred yards away from main part to school (but close to some of the houses). I don't think you could call which one is 'better'. Both are great. The advantage you have with Tonbridge is knowing the house, at Kings if you do get in you will probably not get a choice now.
As for looking round the school, there is an open morning on 15th. They always ask people to register, but I've never once been to an open day and been asked to prove who I am, so why not turn up anyway?
Kings may be more accommodating if you tell them that it is becoming your first choice and not your back-up plan. If you call them, ask to speak to Bev. She's the assistant to Mr Reilly, and very nice.
If you need a back up plan and want to stick to the area, Kings Rochester might be worth a look too?