I have an established service/business I have been running for years, and I am considered an expert in my field. I am rebuilding our very old site, which will have many new features and a membership aspect. Unfortunately, my pricing has remained the same over the last several years, and I have always given away more for free than I should have from a business standpoint. I want to make this a viable business model and compensate myself for the time I pour into it. The new site launch brings so much to the table, but it will also cost more to maintain. How do I raise my prices without losing my customers? How do I price our new products without pricing them out? There is no one else who provides this local service.
There are two streams in your own words
a) You want to increase price per unit of your time
b) You want to monetize freebies
However from the words above I understood that the justification of increasing price is the new site that will have additional expenses to maintain.
I am also assuming you business is to providing services
Increasing the price based on the changes in site can only be so much ( means very little) depending on how important
for your customers is visiting of the site. Services business is more of Word of Mouth spread and repeat customers do not tend to value up scaling of sites much. If your customers come to your site to avail / buy services then upscaling of the site can be redeemed to some extent. This extent is limited to
a) either increase in value the customer gets from the services ( in your case None)
b) customer perceives additional costs / inflation : This is more applicable to you however the increase is limited to inflation factor only (1-2% in developed countries)
So I my suggestion to increase the rate (per unit of time) can be equal to Two inflation cycles (e.g combined inflation of 2 years)
However your biggest monetization is Freebies. this is where you have the scope and this can be based on Freebie or based on Unit of time. We can discuss Freebies and their monetization if you like