Proper way to screw in subwoofer

That would be a no to the velcro route. You have the right idea to build a false floor but instead of trying to bolt it down, screw it down taking care that the screws are not too long and will not puncture a wire or fuel tank etc.

Securing the woofer to the box:

• Position the box so that you can install the sub on the top;  that is, don't try to secure the sub while in the firing-sideways position.
• Center the sub over the mounting hole.  Move it slightly in all directions to ensure that it clears the hole on every side.  Look through the sub's mounting holes to see that there is wood at every hole location.
• Using a sharp awl or thin nail, tap with a hammer at each of the hole locations to mark the starter holes.

If you are going to carpet the box, now is the time to mark the subwoofer frame location.  Draw a pencil line around the sub.  Carpet the box and cut the carpet on the line.  This will allow the sub to fit against the wood, not against the carpet.

• Remove the sub from the box and put it out of harm's way.
• Use a drill bit that is slightly smaller than the shaft of the wood screws that you will use to secure the sub.  Use a drill that has a plumb level (bubble in a window) to guide the drill straight down into the wood.
• Install speaker sealing gasket tape around the circumference.  Cut an X with a sharp razor blade across every hole.
• Push round toothpicks into at least 3 of the holes, which will serve as guides for placing the subwoofer into position.  After the sub has been settled into position, press a toothpick into the starter hole at every mounting location to make sure the starter hole is centered under the sub mounting hole.  Once satisfied, remove the toothpicks.
• Use a good quality screwdriver that fits the mounting screw.  It's best to practice one into some scrap wood to make sure it doesn't slip in the threads.  Screw the sub into place using coarse-thread high quality wood screws.  Select the screws so that they fit nicely onto the subwoofer frame (usually pan head).  If your sub came shipped with mounting screws that take an allen head wrench, use those.
• Position your hand between the screwdriver tip and the sub cone/surround.  You want the gouge (if there is one) in your hand, not the speaker, should the screwdriver slip.  Blood washes up nicely if done right away.

Velcro couldn't hold the sub in the event of a sudden stop (read: crash).  Securely bolted to the chassis, however you want to do it.  As for the crossovers, look into the glove compartment for an answer to where to put them.

Not much more to add to it than that.