Unfortunately the only suggestion I would have is to contact the extension developer and ask them if they can implement URL shortening which is pretty straight forward. Their are other plugins that can provide the URL shortening function and the developer would then simply have to call this URL shortening function when creating the SMS. From reviewing the Wordpress plugin site is seems the developer is quite active with the last update only being a week ago and they seem to respond to feature requests also.

https://wordpress.org/plugins/shorten-url/

I'm sorry that I couldn't do more to assist you on this but unfortunately as the URL's are being generated by the plugin this is where they would need to be shortened in order to cut down on the number of SMS segments being used for sending. With regard to how they are being displayed and broken this is down to the handset and whatever version of Android they have or app that is handling SMS, from the links you have shown in the screenshots it is because the URL is considered malformed. So there should be a / at the end of the domain name http://www.yoursite.com.au/? not http://www.yoursite.com.au? see below:

http://maps.google.com/?q=  -> Will display just fine

http://maps.google.com?q= -> Will display as broken on the phone as it will only show up until the ? as a valid link.

Perhaps this is something that you could raise with the plugin developer also and this for certain is a very very simple fix they can implement even if it still leaves you with the issue of long URLs which leads to longer messages.