Easier on the eyes,

What's missing is a strong pull-down on the PNP. Your logic styles are inconsistent, so the voltages/currents are as well: you've got collector-to-base style TTL on the first three transistors, but then there's the PNP in there. An additional NPN in the same collector-to-base style format would work.
It might be better to use PNP for everything, so you get strong drive into the LEDs, no threshold violations, and you can omit the first inverter since everything will be complementary.
If you're not against TinyLogic (and equivalents), I'd just as well suggest a dual NAND/NOR (e.g., 74HC2G00) to build a basic R-S flip-flop. You also get complementary outputs for free!
A dual NAND/NOR can also easily be built from a couple of transistors. Example:

A pair of transistors can even be omitted if you manage the input-to-base and base-to-ground resistor dividers carefully, so that two logic inputs (and individual resistors) are wired into a single base (and B-GND resistor) to produce either NAND or NOR behavior.
Tim