Since your budget has not wiggle room

have you considered asking the dentist if he/she will barter the difference? You may have a skill or something you can do to “work off” the difference. It might even include things like babysitting for the dentist to have a date night with spouse, personal shopper/running errands–which could be done when you’re doing your own–you charge so much per hour or errand, they pay for the stuff that is purchased.
My recommendation would be to talk to the decision maker … the dentist, not the office personnel who simply process your insurance claim/take your money. Most of the time they are not authorized to make decisions on bartering. When I asked our dentist, after he got done checking my mouth I simply asked, “Do you ever barter your services?” Asking this way, instead of making a statement, “‘I want to barter for my appointment.” made it a conversation instead of a “demand”. Easier to dialog that way. He immediately said yes and we worked out the details for our particular situation.

Now here is what happened last time I went to my family doctor. I make custom coasters. I wanted to gift a set to her with no strings attached. I brought the set with me when I was accompanying dd to the doctor. When the visit was over, I told her I make coasters and wanted to give her a set. (It was decorated with ‘LSU’, a football and a fleur de lis, all in purple and gold with the football being brown. I didn’t ask her to comp the visit but she did. I only realized later what occurred when left and the lady at the counter said ‘no charge today’.