How to hotwire a vehicle faster

I'll repeat myself again(as in the comments).

I don't know about GTA5, but in general SSD would be faster than a normal HDD + BluRay. PS3 uses SATA1, which provides a bandwidth of maximum 150 MB/s(SATA2 allows 300 MB/s and more modern SATA3 provides 600 MB/s bantwidth).

HDD used in PS3 slim reads at 65 MB/s and BluRay at around 9 MB/s(all PS3 models use 2x speed BluRay drives). That sums up to 74 MB/s read speed, which is almost a half of SATA1. If you run solely from an SSD you will achieve these 150 MB/s, which is twice as fast as HDD + Bluray.

And I say that running from an SSD will grant you 150 MB/s because of SATA1 limitations, despite the fact that modern SSDs do have both read and write speed of over 500 MB/s.

As you noticed in second video, both load speed and character switching of SSD is (more than) twice as fast as HDD+Bluray(41 sec vs. 102 sec and 8 sec vs. 16 sec respectively).

And I totally agree with Nolonar's comment.

In the answer to this question about garages: How does the garage system work in GTA V?

Taken from the manual: Player characters can own any vehicle in [GTA V] as long they have appropriate storage for it. To purchase a new car they must first own a garage ...

So yes, you must purchase another garage.