So, I've been planning to collect these comments and start adding them as owner-added to the listings. I know these will be taken with some grain of salt, since they're provided by the owner, but was thinking it would help.

It depends on the quality of the review. If it is simply gushing, with no balance, then I tend to reject or minimize it's value. If it's balanced with not only compliments but recommendations, I give those more credence. No place is perfect for everyone, and some recommendations, particularly those you act on and can state as such in your "reply," have a positive impact. For example, a review of our current rental would include the fact that the location and river frontage is just about perfect. They have hit the trifecta of view, sound, and great access, but it was nearly impossible to find a pan I was willing to cook in, and that perhaps fewer of the pans would have a permanent layer of burned food if the dials on the stove actually gave some indication of how high the electric burner is. Now the location, which is perfect anyway, can't really be changed, but a new set of pots and taking a sharpie on the stove controls could remedy those complaints and show the owner to be attentive to the renter's needs.

The other option is to reach out to past renters asking them to do so, but I don't want to bug them too much ...

Bugging them too much is never the answer, but make it easy for them. Send them an email to the effect that you hoped they enjoyed their stay, and would appreciate them taking a moment to review the property to help others decide if this property is the right one for them. Provide the link, and ask them to email you if they submit a review so that you can make sure the review appears and their efforts are not wasted. When you have a few reviews, start the email off with "If you found the reviews to be helpful in making your choice to rent our property, please consider submitting one of your own." Offer a return customer gift if they submit a review. Something like a local product your area is known for or a gift certificate to a restaurant would not break the bank, and reviews would help you get more business.
I know that some people resort to family and friends submitting reviews, which is one way to jump start your reviews, and ethical if honest.

Every time I've been provided a link, I've submitted a review. When I have not, I often forget. I do wait for my security deposit to be returned before I review, however.

IP