I use banggood redcon 4 channel rx's for this sort of thing
https://m.banggood.com/REDCON-CM421-2_4G-4CH-Full-Range-DSM2-Receiver-Spektrum-JR-Compatible-p-1015760.html although the Orange R410X is very similar. I've had amazing range from these (over 500m) when correctly installed away from servos and motors etc. You can also remove the pins and solder directly to them which gets the weight down to around a gram (the pins and servo plugs are where the weight is.)
I'm not sure if they will bind to the TX you mention - it probably depends on the age. I seem to remember the newer models can rebind to a DSM2/X transmitter so it may be possible. If you intend on building a few models like this it's well worth getting set up with something like a Spektrum DX6i which has model memories and some basic mixes.
All the DSM2/X receivers should run on 3.7V but you need a decent capacity battery to avoid low voltage. The brown out voltage is then avoided. I would suggest 300mah since you will need the noseweight anyway.
Servos depend on the size of the control surfaces, a good servo torque calculator can give an idea (online ones available) but anything from a good 2.5g Emax ES9251 through to 4-5g servos such as ES9051, Gening or Turnigy 1370A depending on the size of the model and budget.
85-95g is a low target weight for a 1m DLG, the Elf is 95-100g and is exceptional. The Strike 2 is 110-115g. My own solid wing 1m came in at 140g but was designed to be beefy

I would also use pull/spring control rather than pushrods and save some weight in the tail.
Look forward to some pics!
Jon