It looks like the resistors R4 and R3 set the timing of the phase 2 signal, besides simply pulling up the outputs of the inverter gates. Gates D and E (the ones with pins 11,10 and 9,8) would work fine if you used a 74x04 and removed the pull-up resistors, but the other two gates being open-collector is integral to how the clock generation works.
There are ways to design an oscillator around a non open-collector inverter, though. This example refers to CMOS inverters but you might be able to tune it for 74LS with some experimentation.
https://www.falstad.com/circuit/e-inv-osc.htmlAnything you have on hand that can generate a square wave should work, though. 555 timers, crystal osc modules, Schmitt-trigger inverters, can be used for instance.
EDIT: Nevermind, I didn't look closely enough at the schematic. Basically disregard everything I said.