Anything is possible when you're a coder!

Just have to split the downloaded HTML into patterns and extract the data you need. You could get some books on learning BASH, sed and awk and do it yourself or hope someone else will be interested in using the site and write the script for your.

There are a couple things you can do to make websites faster on the tablet.

1) Turn off Javascript before opening the page. Some sites might not work properly when disabled, just turn it back on when using them.
2) Turn off images before opening the page. Sadly, that site does not support blind users (no alt tags on the download and listen buttons). This means you need images enabled in order to click the download button. If you know any Javascript you could try writing a bookmarklet that finds all of the download images and adds an alt tag. This is untested but might work, don't add any spaces.
3) Blacklist social and tracking IPs in your /etc/hosts file. Load the site in Chrome, click the cookie icon in URL bar and show all cookies. Add each one to /etc/hosts after "127.0.0.1 " with one per line. Don't add cookies for the site itself or any social networks you want to use or you won't be able to load anything from them. Some images might be loaded from dedicated image servers and those can be blacklisted as well. Getting rid of the third-party cookies reduces the number of remote requests and in many cases removes ad images at the same time.
I would have posted my blacklist but my router currently has a corrupted config and wifi isn't working, and not going to copy them by hand.