I would keep calling Verizon and bug them about it. Get your neighbors to, too. Maybe they'll listen.No. We barely have phone service in our driveway. Verizon doesn't think a small farming community needs a phone tower. Been this way for 20 years.
Contact your cell carrier and see if they'll provide you a cell extender. These are small "mini cell tower" devices that provide cell service through your internet connection. Sometimes the carrier will provide for free to avoid cost of improving signal to your location and to get you to stop complaining to them.
The data foot print, i.e. the size of the data transmitted to the car, is probably on the order of bits (probably just an encrypted token with a config flag). So the download speed of the signal strength in the garage is irrelevant also. Even if you see 2G speeds in the garage and the remote start package is 100Kb you are talking 1 second to download.
I've also questioned whether the cellular bandwidth is the contributing factor for how long it takes from the request (start, unlock, etc) to vehicle actually executing request. I agree with @MrMegaDeath that the amount of data for the start signal is probably minimal (a couple hundred bytes at most).
More likely ...
1) To conserve battery/power, the vehicles cellular modem (VCM) is not maintaining cellular connectivity continuously . The VCM is powering up every X seconds and "phoning home" to see if it has an request/action/message. For example: If X = 60 seconds then request and vehicle actually executing request would vary from 1->59 seconds.
2) The Hyundai/Genesis service (probably in the cloud) is overloaded/poorly architected, adding to the delay.
Curious, what is it, what do I ask for? I'm with TMO and have a friend on my plan, but he gets bad reception at his house. It's the old Simple Choice plan where I can add a line for $10/month.T-Mobile will give these to customers for free. I needed one for my office since we are farther out of the normal service area. Also have one at my parents house even thought there is a tower 3/4 of a mile away, their house is down in a small valley and the signal barely reaches their house.
Check this out Signal Booster vs. LTE CellspotCurious, what is it, what do I ask for? I'm with TMO and have a friend on my plan, but he gets bad reception at his house. It's the old Simple Choice plan where I can add a line for $10/month.