Am running a similar setup on a bigger rig.
Minivan with FZ07.
400 lbs+ rack is allot hanging off the back of a small 4 cylinder miniSUV.
Some points for you to consider.
Can you get a class 3 hitch for a CRV? Tongue weight capacity is the important thing here. Your motorcycle weight will be leveraged off the back increasing that weight on the tongue. IIRC, class I hitch only has a 300 lb max tongue weight rating and a class III has a 500 lb. Add the bike and the hitch weight and your at...
My carrier had it stuck out too far increasing that leverage weight. Chose to move it in by drilling another hole to bring it in 4-6" closer to my rig and reduce that leverage effect. And added reinforcing bars to the frame as the single bar support system wiggles allot and is not very solid nor confidence inspiring.
Can your suspension handle that extra weight cantilevered on the back? My minivan barely does and it is a bigger, more solid vehicle with a higher load carrying capacity. I had to add air bags and air shocks to better handle the load and I drive cautiously. If you have IRS, could be tricky.
Tires are an issue here as well. I have stock size and premium with a high weight rating for it's size and would recommend going max on that. Tire size and rating could be another limiting factor.
These safety issues are Very important.
Police haven't been an issue for me here out West but need to relocate license plate and added auxiliary brake and turn signals that can be seen properly since the bike hides them. Probably not the same back East where they are looking for reasons to stop you and keep their metrics up.
As well, I cover mine with a Moto cover and strap it down with heavy duty straps, six of them. Don't use the orange straps from harbor freight, only rated for three hundreds lbs. Use 500lb+ straps. Putting a cover helps to deter as it means more work to get the prize.
IMHO, the CRV is on the light weight side for this in size and power but if not going far or putting around, might be ok. Think a small trailer would be a safer,
better way to go for your rig. Think auto is rated for 1000 lb towing capacity.
Don't know if you will find a class III hitch for your vehicle as it exceeds the capacity of the vehicle and not safe nor recommended. Also would recommend downsizing to a 250 dual sport which should weigh in at about 250 lbs, more realistic and safe for a hitch setup.
Many things to consider...