VE7TGT,
Welcome to the wonderful world of the Amateur Radio Service....i.e. Ham Radio!
I'm sure you will love it, and grow into, and learn a lot....and, have fun.
I hope you don't mind some friendly / helpful (but very blunt and direct) advice and answers to your questions....because it might sound harsh, but below are the facts!
1) The issue of a 7' antenna height clearance for your truck antenna is a rather moot point for your question....'cuz what you wish to accomplish is all but impossible, using the equipment you mention. (But, read below for ways that you could make this communications work....and, yes, if you bend a long whip over, in an upside-down U shape, it will fit in/under a 7' clearance garage...)
2) As I understand it, in addition to participating in all the incredible aspects of our wonderful service / hobby of ham radio, you desire to communicate from your 3rd floor apartment to/from your vehicle (truck of some kind) when out on remote forest roads, mainly over distances of 200 - 300km (150-200 miles)? Yes?
You are
not going to be able to do this with a handheld ham radio / VHF-UHF "handie-talkie"! This is
not possible (unless by some miracle, there were a series of repeaters / linked-repeaters along your routes / remote forest roads, that were also connected/linked to repeaters in town near your apartment...and, even if all of those were installed and available, it would be a one-in-a-million chance you could reach them with a handie-talkie.....in short if this were the case, there would already be much infrastructure along those routes/roads and there would already be cell service.)
So, this is
not going to be possible, at all!
Although, if there were some good, wide-area-coverage repeaters in your area and along your entire route/path, there is a slight chance that a couple "50-watt" VHF radios with good antennas, might make some contact....
I have no idea what type of terrain you're driving thru....nor what, if any, VHF Ham repeaters are available along your route....but, my guess is it is VERY doubtful this would provide the communications you desire.

3) However, if you were to equip both your truck and your home with HF radios and antennas, to cover both the 80m and 40m ham bands (and possibly 60m, etc.), and had good low-noise-level receiving at your home (that is a challenge, especially in an apartment!), then you could be all-but-certain to be able to maintain contact from your home to/from your truck, along a 200-300km route, along remote forest roads.
The type of communications you'd be using is called High-Frequency Near-Vertical-Incidence-Skywave (or HF-NVIS) comms....which generally takes place between ~ 2mhz and ~ 9mhz (although freqs as high as 12mhz are used in certain areas of the world, primarily by gov't/military), and along paths/ranges from ~ 20km out to 300-500km...
It would be rare to be able to use the same band / same frequency both daytime and nighttime, along the entire route/path, so provision needs to be made to have a "primary" and "secondary" band/freq pre-determined...
(also, be aware that much longer distances can be covered using the same equipment, depending on time-of-day and selection of band/freq, antennas, etc....we can get into those details later, if needed)
The details of this equipment, especially the antennas needed, is important....and, I will give you more details if you desire (but, I sense that you are not fully aware of what this will entail and are probably not well-enough experienced with HF Radiowave Propagation to grasp the intricacies of the "whys" and "hows", yet..)
So, I'll just give you some very basic info here:
--- For both your home and truck, you'd need a decent modern 100-watt output HF radio....(depending on make/model, etc. figure approx $1000 USD each, for a total of ~ $2000), in addition at your home you'll need an adequate power supply to power the radio (~ $200 USD)....
--- Antenna on truck can be a simple 102" CB whip (or a longer one, if possible), fed with a remote tuner/coupler such as an Icom AH-4....(figure on ~ $400 for all of this).....and, you can bend the whip into a big upside-down U shape, by feeding the base and pulling the tip down with some rope over/across the top of the truck to better produce radiation as close to straight-up as possible.
--- For your home....you will need access to the roof of the apartment building, or even much better access to some trees a way away from the building, that you can run coaxial cable to....and build/install a 40m/80m "fan-dipole"....trying to get the feedpoint 30' - 50' above the ground, keeping the 40m wires no more than 30' - 40' high, but getting the 80m wires as high as possible (keeping them below 70' high)....(figure on ~ $300 - $400, plus any mounting supports/hardware, for the antenna wire, balun, insulators, coax, etc....depending on where the antenna are installed)
Adding this up....figure on $2500 to $4000 USD, if buying new equipment and doing all the installation / wiring yourself.
BUT....
But, the single most important part of the whole system is YOU and THE OTHER PERSON (at home)....you both must be licensed hams, and have a decent understanding of HF Radiowave Propagation, HF communications procedures, etc.So, you see it is do-able....it just isn't do-able the way you initially thought!
4) If the requirements above are too much, then you other option is Iridium sat phone....an Iridium 9555 phone, with car-kit, etc. will set you back ~ $1000 - $1200 USD, with airtime of ~ $1/minute....a simple mag-mount "puck" antenna on the roof of the truck, connected to the phone in the truck, and you're good-to-go for world-wide voice calling and SMS/text messaging 24/7/365, to/from your phone! Easy-peasy!
(the 9555 battery will last a few days on "stand-by", waiting for a call....or you can power it from the 12vdc of the truck and/or charge the 9555's battery from the truck)
FYI, in addition to having ~ 50 years experience studying and using HF radio / HF Radiowave Propagation, etc. etc....as well as mobile operations (mostly HF maritime mobile and VHF ham mobile....but some of both and the other, too), I've also owned/used Iridium for many years now...
I do hope this helps? (and, if you desire more details, ask)
73,
John, KA4WJA