Use an ordinary cord as a cheap inlet
What the ---
--- sigh. I get it. NEMA 14-30 inlets are pricey. So....
Find an appliance cord of appropriate ampacity, with the plug that you want for an inlet. This can be salvaged off a broken appliance or just bought (e.g. NEMA 14-30 dryer cord).
Take it into an electrical supply and get a strain relief that allows that cord to enter a 1/2" or 3/4" standard knockout on a metal box. Figure $3-4.
Get a blank faceplate with that knockout, or better, a metal extension box for the box your "suicide" socket is now.
Install the cord into the strain relief, put that into the knockout, and wire the end of the cord into the circuit.
Look at that. A house connection that's a plug, not a socket, and didn't cost an arm and a leg. Now we don't need a suicide cord.
Mind you this is probbbbbbably a Code violation (I haven't really split hairs on 400.7/400.8), but it beats the living heck out of a suicide cord.
Wait. But now I need a 14-30 inline socket.
Well you already had a 14-30 socket, now you just need a new box to mount it in. That's fine, get an appropriate steel box such as a 4x4 deep box ($2-ish at electrical supply) and cover, and mount this right next to the above "inlet" and within reach of the cord! Got it? Out the bottom of this box, bring a common NEMA 5-15 plug/cord. So it's a double inlet that lets you swing either way.
Or you could just shortcut this and do the 5-15 cord straight.
DO NOT tolerate cords draped through cracked-open doors or windows!!!
I know you think the suicide cord is the dangerous part here, but you're missing the big one. Many people have generator inlets inside their house yet they run their generators outside. This inevitably leads to cracked-open doors to let the cord through, and this lets in carbon monoxide and kills them all. link 1 link 2 During hurricanes, generator stupidity is already the #1 killer of people, and often the only killer of people.
So I know you're expecting a smackdown for the suicide cord, I really need to give you a smackdown for the interior generator inlet. Move it outside. Cheap cord trick and all. I really don't care how, because anything you can do is less dangerous than an indoor generator inlet + suicide cord.
Your real question
OK, so USA power comes in 2 "poles" of 120V each, totaling 240V. Here is a wonderful video that also gives Europeans some snark (in other words: delightful). That video touches on how things are phased in the panel, but this answer goes into more detail.
These 2 poles means that your 120V generator is only feeding one pole. Can we fix this? Yes probably, but we MUST do an important step first.
Part 1: identify Multi-Wire Branch Circuits
This part is an absolute prerequisite, because we need to not set your house on fire. Your house may not even have any but this must be checked for.
Multi-Wire Branch Circuits (MWBCs) are 120V circuits where 2 hot wires share a neutral under controlled conditions, which do not set the neutral wire on fire. It is absolutely vital these be phased correctly. Current Code requires they be handle-tied, which on all but GE panels also assures they are correctly phased. (On GE panels best to use a 2-pole 240V breaker.)
I know you want to call them "2 circuits shared neutral" but they are actually 1 circuit with 2 hots.
So you need to search each circuit in the panel looking for any evidence of MWBCs. Typically a /3 Romex with red and black going to different breakers. Might also be a conduit with more hot wires than neutral.
Take special care that every MWBC is correctly phased (240V across the hot wires is correct), and every one is identified with a handle tie. This is essential for the next part.
Part 2a: there positively are not any MWBCs.
If you are positive your panel has no MWBCs, then you can do a simple thing: wire your one hot to feed both hots on the 14-30 socket. I know you're really tempted to do this without searching for MWBCs. Don't.
Part 2b: MWBCs identified.
Now you understand phasing and know where all the MWBCs are, you can move circuits around so the circuits you want are all on the same phase. For MWBCs, simply exchange the two hot wires. For others, move breakers around - you don't even have to disconnect their wires, you can rock them out and leave the wire attached.
If you need both legs of an MWBC powered, you have no viable option except a 240V generator.
Now with all your critical circuits on the same phase, wire your generator cord so that the generator feeds that phase.
