Help? Problem With Holding The Groove On A Hot Pressing

Is there any plausibility that these hot grooves found later in a side would be a result of the physics of cutting?

None whatsoever. The physics of cutting is that the cutterhead responds exactly the same to bass notes at the beginning of the LP as it does at the end. It is simply moved across the lacquer as the signal is played through the cutterhead. There is no compensation in the electronics for its location on the LP, just the compensation for the cutterhead response (being an electro-mechanical device) and the imposed RIAA curve. 

My question is; how do you "adjust" the resonant frequency? My current values for vertical are: 15 Hz - 7Hz. My lateral values are 14 Hz - 10 Hz.
Should I even worry about trying to match the vertical and lateral exactly?

To the latter- no, as long as its in the window of 7-12Hz. The mechanical resonance is not really adjustable on your arm- the way to affect it is to change the cartridge to one of a different compliance or to use a lighter or heavier headshell.

They never match perfectly which is OK. I shoot for averages between 10 and 8. You lower the resonance frequency by adding weight to the head shell and raise it by subtracting weight. You can get head shell weights that fit under the cartridge or you can add nuts to the screws etc. Subtracting weight is a bit more difficult. Get out the drill. Warning, if you get down to 3 Hz record warps will send the tone arm skywards! Use the anti skate test track to set the anti skate. If you lift the anti skate weight while playing that track you will notice all the distortion go to one side. If you add too much weight the distortion will go to the other side. You adjust it until the distortion is the same and minimal in both channels.

Thanks,
If adding or subtracting small amounts of weight to/from the headshell changes the cartridge resonance, why wouldn't adding or subtracting some tracking force accomplish the same? The physics must be different?

why wouldn't adding or subtracting some tracking force accomplish the same? The physics must be different?

Yes. Triplanar arms are supplied with counterbalanced weights of different sizes. You can use one or multiple weights with different distances from the pivot bearings- and so effect the effective mass and thus change the mechanical resonance. Weights in the headshell are more effective if you need to lower the resonant frequency, going the other way is why Triplanar makes the multiple counterbalance weights. If using a spring loaded arm you can move the counterbalance weight and set the spring differently, but the scale on the arm won't be correct anymore- so you have to use a cartridge tracking weight scale to know if you're at the right tracking pressure.

When you change the "weight" of the needle in the groove you are not changing the mass so the resonance frequency stays the same. It is very common to confuse weight with mass. Your tonearm has the same mass in outer space but it has no weight! 
When adjusting the mass of your tonearm system you are trying to get the resonance above record warp frequency (about 3 Hz) and below the lowest frequency recorded on the record around 18 Hz. 10-11 Hz puts you right in the middle. My records have been stored upright under pressure for decades so I very few warped discs plus my SOTA Cosmos sucks them right down so I try to keep the resonance frequency even lower 7-8 Hz. I think this improves the Bass but frankly I have not been able to AB this so it might be psychological:) What I can state as a fact is that if you let it run to high over 18 Hz you will destroy your bass, possibly feedback and send your tonearm skyward. I once knew someone who installed a Koetsu in a Transcriptors Vestigial tonearm and he wanted to know why his tonearm would not stay on the record!