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