I travel a lot too (husband works for an airline).
Flying transatlantic, airlines tend to be cool with a suitcase that fits to their measurements plus another small item such as a briefcase or handbag. I always bring a case that fits the maximum allowance, plus a handbag. I also commonly see people with a suitcase and two or even three (!) other small items, like a handbag and shopping bags from duty free, but I stick to the one-case-one-personal-item rule. It's been very inconsistently that my carry-on case gets weighed, so you have to be prepared for that. Long-haul carriers tend to be very accommodating though!
I've flown recently on RyanAir and EasyJet, and RyanAir was less strict, allowing a (small) carry-on case and my handbag. EasyJet in the UK had no problem with the same exact thing (small case and handbag), but coming back from Barcelona, the ground staff made me stuff my handbag into my case. I can't say 100%, but I'm pretty sure EasyJet has no weight restrictions on the stuff you carry on.
Gatwick is pretty consistent with asking you to take out laptops and tablets, and seem to be okay with leaving e-readers in your case or bag. I've had variable experiences at Heathrow, but to be fair I don't bring a laptop often when I travel.
Oh and I second the idea for the luggage strap- great idea!