I've had the same problem too. I've chosen to use gritty realism but instead of 7 days for a long rest, I've reduced it to 24 hours.
This way if they really have to, the players can still take a long rest during a session but they need a safe haven and their ennemies can take advantage of this time to get prepared.
Something along these lines seems like it would be the best option. The problem with the default 'gritty' rules is that it is likely to change the ratio of short to long rests. The normal rules usually net 1 or 2 short rests per long rest. The 'gritty' version would probably result in at least 4 or 5 short rests to each long rest, thus making the short rest reliant classes shine more than they normally would.
Also, spells with a fairly long duration that are meant to be recast-able every 'day' suffer a little in the gritty mode and may need to be taken into account: Mage Armor is one I can think of off the top of my head. One may be hesitant to cast these spells if they know that they are not going to get the slot back the next 'day' (Arcane Recovery notwithstanding).