you can have a single data-widget-id and filter out any tweet message feed by just adding,
data-screen-name="AnyTwitterName"
for an example
<a class="twitter-timeline" data-widget-id="6596840392xxxxxxxx" data-screen-name="AnyTwitterName" ></a>
use
twttr.widgets.load();
if you have loaded //platform.twitter.com/widgets.js already
In my situation I doing like this: replacing content of some empty or previously timeline filled block to new link like yours
<a class="twitter-timeline" href="https://twitter.com/vinto60utd" data-widget-id="283564783750483968">
Tweets by @vinto60utd</a>
then I call twttr.widgets.load();
and twitter do the rest.
You can create widgets at run-time using Twitter for Websites JS.
https://dev.twitter.com/web/embedded-timelines
Change
!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0];if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src="//platform.twitter.com/widgets.js";fjs.parentNode.insertBefore(js,fjs);}}(document,"script","twitter-wjs");
To
function twit(d,s,id){var js,fjs=d.getElementsByTagName(s)[0];if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src="//platform.twitter.com/widgets.js";fjs.parentNode.insertBefore(js,fjs);}}
twit(document,"script","twitter-wjs");