Yes, a PNP (transistor) can perform the inversion from LO to HI - probably need a resistor or two to surround it. Maybe 25 cents of parts but probably requires firing up the soldering iron. And, yes, it would replace the 1st relay (inverter). But with the addition of a 10 cent capacitor, you could then replace the FRM01 and use the 1st relay. I found this diagram in a folder of old stuff but couldn't find the OGR thread that describes it 
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This was a non-inverting (using an NPN) transistor with DC+ on the outer rail and a HI trigger relay module. I even have a video of this in action on a relay module showing this leads to a 30 second delay (delay time adjusted by the capacitor value). Driving me nuts I can't find the OGR thread! Anyway, if you're interested I will re-draw this for an inverting version using a PNP transistor. That would replace the 1st relay module.
But if messing with adding discrete components anyway (transistor, resistors), why not add a 10 cent capacitor so that you can essentially convert the 1st relay module to a time-delay relay module. This would eliminate the FRM01. The key is the transistor which provides current-gain that essentially amplifies the effectiveness of the capacitor to keep the relay closed during loss of trigger. This allows delays (hold times) of seconds using reasonably sized/priced capacitors.
