Yes, without doing the new TTK raid your best option to get higher light gear is doing the strikes .i.e. the Nightfall strikes. Those can drop stuff >300.
Or start farming ultras with a Three of Coins activated and hope for an exotic 310 light lvl drop.
On the other hand try to find a group for a PS4 raid via the Bungie or reddit forums and give it a try this way.
If you find nice people the Destiny raids are one of the best MP experiences I' ve ever had on any gaming platform!