My two centavos:
The best security is a vented enclosure or a truck bed cap that has open windows on the sides. Out of sight, out of mind, and a thief would be having to crack into that, then start cutting the chain holding the generators in the truck bed.
On my Yamaha generator, I use security chains and a padlock imported from Germany (Europe has a "sold secure" vendor-independent authority that locks have to get graded by, especially if they are to be used as "insurance locks"... i.e. enough security for European insurance companies to pay a claim.) Not anywhere near 100% security, but it is good enough that a thief will have to fight for it and I made a good faith effort in keeping the generator secured if I have to put in a claim.
The dog kennel thing is a good idea. Maybe put a hole in the bottom so you can put a security chain through that isn't noticable, so you can chain the generator down in the kennel, so if the camoflauge fails, there is still the security chain to deal with.
In any case, I highly recommend springing for the reinforced handle kit. It can only help.
The Lock Down baseplate as mentioned above has good security... but you will need a very good place to anchor it to. I can see a hitch mounted cargo rack. losspreventionfasteners.com sells bolts which the hears shear off at a predetermined torque. By using those with a well made cargo rack (and putting Loctite Red on the fasteners), the Lock Down baseplate is not coming off unless someone cuts the rack off the hitch. That might be an idea, except the generator is definitely in plain view for all to see.