TMZ's learned that the release of Lin-Manuel Miranda's masterpiece has resulted in renewed interest and traffic for several leading theater-streaming services ... and people are wanting to get more than just their "Hamilton" fix.

A spokesperson for Filmed on Stage, the largest online database for filmed Broadway musicals and plays, tells us ... its website saw a spike of nearly +250% in the 2 weeks leading up to the July 3 premiere of "Hamilton."

We're told traffic peaked on that Friday -- with an increase of nearly 400% compared to an average Friday -- and interest in the site's filmed Broadway Musicals section has been steadily increasing ever since ... from users all across the U.S.

Filmed on Stage says its most popular titles this past week include "Newsies," "Rent" and "Kinky Boots," but it's also been receiving hundreds of emails from users asking why their favorite Broadway show isn't available to stream.

The rep tells us ... "While we are used to receiving such emails, I can safely say we received an unusual amount in the past week with visitors mostly asking for other hit Broadway musicals -- 'Wicked' leading the list."

Thespie is another streaming platform that allows visitors to discover more than 1,000 theater performances. A rep for the company tells us total traffic has increased by 86% compared to last week ... largely based on people searching for where they can watch "Hamilton."

We're told views of all the "Hamilton" and Lin-Manuel resources available on Thespie have increased by a whopping 277% since July 3 ... while non-"Hamilton" titles are also up 62%.

Of course, with Broadway shut down for the rest of the year amid the pandemic, these streaming services are more important than ever to keep theater fans satisfied ... but the "Hamilton" hype has certainly given them a shot of adrenaline.