If you're desperate to have exactly one and only one address in Electrum... I would suggest creating a new "standard" wallet with the 12 word seed backup... then export the private key for one of the addresses created at start up... and use that to create an imported wallet.
After creating the "Standard" wallet and writing down the 12 word seed, you just click the "addresses" tab ("View -> Show Addresses" if you can't see the tab), then right click on any of the addresses shown as "receiving" and select "private key".
Then create a new wallet:
- "File -> New/Restore"
- "Import Bitcoin Addresses or Private Keys"
- Enter the private key you copied above
You will now have an "[imported]" wallet that only contains 1 private key... but can be "restored" at any time by using the 12 word seed backup. You can even delete the "Standard" wallet file so you don't accidentally open it in the future and get given a "new" address.
For the record, I don't recommend doing any of this... but if you have a real requirement for a single key wallet, it'll still give you the simplicity of a 12 word seed backup.
If you just need to be able to "re-use" addresses... then just use a "standard" wallet in Electrum, give people one address and go for it... Electrum doesn't care if someone sends coins to the same address multiple times... the addresses don't "expire".
The whole "payment request/invoice expiry" thing is confusing and unintuitive... just ignore it.