That was flying with AirAustria from Heathrow. As you say, London flights are cheaper. We live in the southwest, and our regional is Bristol, but Heathrow is easier to get to as Bristol is in the back end of nowhere and often tends to be the more expensive option.
We've found that if you just take carry on these days, Easyjet has stopped being the competitive option.
In terms of booking your flights via EJ. We were booked for Christmas 2021 (cancelled due to testing requirements), and those flights went live around the 1st of April. So, it's not long to wait and plenty of time to find an alternative.
Don't forget too that other airlines have a more flexible hand luggage policy. EJ are strict on their ONE bag per person unless you've paid the premium or have squashed it into a duty-free bag (all policies seem to stop then).
Last year, I flew with AirBaltic to Riga, Lufthansa to Munich, and Air Austria to Vienna.
For AirBaltic and Lufthansa, I had my Kanken backpack that I use as my handbag in addition to my wheeled case, so not a small backpack.
Coming back on Lufthansa, I had my ski boots in a shopping bag, too, as I'd bought them there. Nobody said a word to me, though I was expecting to be stopped and charged.
For AirAustria, I had the same backpack and my helmet in its drawstring bag, DH had a backpack, and we had a Bag for Life with snacks in for the DC.
All of those airlines allow you your case + one under seat bag, so across six of you, that's a fair amount of luggage allowance.