Hi Martin,
Save your money, time and effort!
Just like my DX6 your TX needs 6V from Alkaline batteries.
To get 6V from NiMH you'll need 5 cells, which you haven't got a cat in hells chance of squishing in. A fully charged 4 cell pack may show up to around 5.6V OFF LOAD.
So you start around half a volt short in the first place.
Shortly after a load is applied the cell voltages will drop to their nominal 1.2V.
Giving 4.8V for the TX. This is roughly the voltage of 4 nearly flat alkaline cells.
2000mAH cells have been recommended.
Good quality Alkaline cells made to the IEC standard, such as Varta or Duracell, have a capacity of around 2500mAH. Make sure you get the Heavy Duty version, i.e. for cameras.
These will last for ages, unless you forget to turn it off ๐
When I tested your TX the switch was perfectly OK and I don't think you can get a toggle switch in without major surgery anyway.
I'm not fan of slide switches either, they are always the first thing I have to replace in Gisela's garden lights and fountain pumps etc, usually due to corrosion. But considering the low usage, without getting wet (unless you fall in the pond with it๐ฎ), it will have in your TX it shouldn't be a problem.
The reason your rechargeables kept popping out is that many of them are a fraction larger than the alkalines. I've had this problem with several
devices
.
I use alkaline in my DX6 and my Turnigy clone. No problems.
The only TX I use NiMH in is an old Graupner MC-10, 40Megs for my submarines.
But it was designed for use with a 9.6V pack in the first place and has a charging socket.
Does your DX5E have a charging socket? No! Neither does my DX6.
Cheers, Doug ๐