I think you will find that the extra run time you get out of the battery between 3.3 and 2.X V may not be worth the trouble of adding a step-up converter. Depending on cell parameters and temperature, you might only get 10% more out of the battery. Also, your proposed step up converter would be quite inefficient.
Some cell phones put a supercapacitor in parallel with the battery to support the 2G transmit current pulses. You’ll need quite a bit of capacitance to do that.
How about you stick with the basic battery connection and work to reduce the load current of everything else in the system? The Quectel module is 2G. That’s old technology and I haven’t downloaded the data sheet, but I see that the supply current says ‘as low as 1.3mA.’ That’s huge in a battery powered system. Have you looked at the new Cat M1 modules? They are designed for low power low data rate deployments.
Finally, a word of caution: if this product is going to be handheld or carried on a belt pouch (or, worst of all, held up to your head), you’ll need to do Specific Absorbtion Rate (SAR) safety testing, which is a giant pain in the ass. If you need that, you should start designing your SAR test right now. I have heard tales of engineers in tears at the test lab when they couldn’t test (and therefore could’t sell) their product.