You could also offer some kind of incentive or compensation, such as a discount on rent for the month or a gift card to a local restaurant or store.If your tenant is still unwilling to allow showings within a reasonable timeframe, you could try to find a new tenant without showing the property.

But I'm wondering if that might not serve as a screening value as well. i.e. anybody that is unwilling to pay online may not be the best payers?

In northern NJ it seems as its still a sellers market but a lot of sellers are just so used to a certain price and buyers are unwilling to pay so it just sits.

1) your tenant does not have direct access to the deposit account; 2) you stop partial payments or over-payments; 3) it creates a trackable account ledger; 4) if your tenant is unable to or unwilling to pay rent, you can initiate a charge; 5) if there are insufficient funds you're not getting hit with charges as you would if you tried to deposit a physical check that bounces.  

I am not unwilling to pay the extra if those with experience believe it to be prudent. 

If you are unwilling to live with the risk, do not purchase the property. 

What if I have tenants coming off a 1 year lease and are unwilling to sign a lease amendment to begin RUBs?

If your attorney is unwilling to stand up for you, then I recommend getting a second opinion.

A smart agent typically won't invest their time and expertise (or share their best opportunities) with someone who is  unwilling to commit to use them for the transaction up front. 

If your property manager is unwilling or unable to enforce your lease (or submetering) you need a new one, period.