I'm where you guys are (well, 265, so close). You're gonna have to bite the bullet and bash your head in trying to do the Nightfall, the Heroic Strikes, or other milestones for powerful engrams, plus loading Legendary Mods into your gear. I think that if you can get past 267 (just my guesstimate, I'm getting 258 power blues at 265), you'll start getting blues that you can infuse into stuff to raise its base level again, but where you are now you're stuck if you just try and do the same content you did before.
Honestly, it's so frustrating, because when I'm playing the game I absolutely adore it but it's just riddled with these baffling nonsense design decisions. Why put the recommended scaling level for the next-level content 10 levels above the best gear you can get without it? Where's the sense in that?
For leveling up without raids or DLC the best way is create 3 characters. One of each class. The weapons that you level on one character automatically increase the power level of drops on the others.
Level each to 265 by doing Public Events, normal strikes, and crucible matches , and by crafting +5 legendary mods and infusing every piece of armor and 3 weapons with them which should get you to either 265 or 270.
Then on each character do the following, all on one character then on the next for maximum leveling.
1. Flashpoint milestone
2. Call to Arms milestone
3. Nightfall milestone (get someone to carry you if you want/can to make this faster)
4. Heroic strike milestone (same)
5. Clan XP milestone
In between turning in each milestone check the drop level of legendary engrams from Token vendors such as Shaxx. If the level has gone up and it's possible you could improve a slot, buy items until you have all slots at the best they can be.
Do not turn in the clan xp milestone this week as it's bugged until May 29 patch.
It will auto decrypt Tuesday and help.
Doing this every week on 3 characters would get you to 290 after a few weeks at which point you can do the normal mode Raid.