This isn't nearly as big of an issue as you're thinking.
The answer I can't seem to find here - and elsewhere - is how much is too much, when it comes down to setting an antenna apart from one's shack?
The effect of a longer feed line between your transceiver and your antenna is increased loss — the signal will be weaker at the destination.
If you are transmitting, this means that less of the power from your final amplifier (whether built into your radio or external) reaches the antenna and radiates. Thus, the consequence of the loss is exactly the same as if your radio had less power output — not anything inherently bad.
If you are receiving, this means that less of the power gathered by your antenna arrives at your receiver. This is problematic if the signal is too weak for the sensitivity of your receiver (but that is unlikely for HF operation) or if you have sources of interference near your receiver that are stronger than the signal (this is something you can avoid).
The way loss in a transmission line works is that, at a given frequency, over a given length of the cable, a certain proportion of the energy will be lost (dissipated in heat or leaked out). Since this is a ratio, it is easily expressed in dB. For example, Times Microwave LMR-400 (a model of coaxial cable popular for high-end amateur use) specifies that at 30 MHz (the high frequency end of HF), there will be 0.7 dB of loss in 100 ft of cable.
In order to calculate loss for a particular length, you just multiply it (given that it's in dB).
$$0.7\,\text{dB} \cdot \frac{350\,\text{ft}}{100\,\text{ft}} = 2.45\,\text{dB}$$
So, with this cable you would have 2.45 dB of loss. That's not bad at all — compared to the average ham's setup, you'll be more than making up for it with your advantageous antenna location and height (assuming you put up a modest tower).
(If you were operating at higher frequencies — VHF or UHF range, say — cable loss becomes much more of a problem. But here, having a clear line of sight from your antenna makes even more of an improvement.)
You can also do better than coax, for HF operation. If you use ladder line (two plain wires separated by insulating spacers), you will get less loss at a lower price. The primary disadvantage of ladder line is that it will not work properly if there are nearby conductive objects, but that is not at all a problem for a long outdoor run in open air (not along the ground). It is also not suitable for higher frequencies as the spacing of the wires must be much smaller than the wavelength and consistent.
The above is assuming perfect SWR — that is to say, if you have an antenna that is built for the frequency band you are operating on. If you want to use many different bands with a single antenna, you will need an “antenna tuner”, and depending on the precise relationships there will be more loss in the section of feed line between the antenna and the tuner. You can reduce this problem by installing a remote-controlled/automatic tuner at the antenna end rather than at your transceiver.
I understand that in order to properly resonate, my entire system, i.e. radio + cable + antenna need to be in harmony and everything has to be thoroughly calculated.
This is false. There are badly-designed systems where every part influences the characteristics, but you should avoid that (and they would be nearly impossible to “thoroughly calculate” because you would need more information than you can practically gather and compute for the model). In a properly built system, the only shape and lengths that matter are those of the antenna itself (and its immediate surroundings — which is why you mount an antenna up high to avoid them).