It seems to me that one piece of important information is “why?” and you need to consider your budget and the time frame and time frame for work.
Providing you use a fluid layout similar to the amazing Matthew James Taylor layouts, which will resize to fit the available screen size. The only reason I can see that mobile templates require a specific CSS style to make your looks more like a mobile app.
I do not see performance as a problem. If you have performance overhead from an existing website, and you are developing these performance issues for mobile devices, then why not solve these problems for non-mobile users. that is, to create a mobile site with the layout of liquids and make it work for viewing desktop / tablets. This may be a good opportunity to redesign the entire site to be more productive.
I see that you really have two options, depending on the budget and time scale.
1) Create an entirely new set of templates while developing performance problems using a liquid layout to switch existing layouts to new layouts over time
2) Redesign existing templates and functions to make a mobile site.
In any case, users of your desktop and tablet will benefit, but how far you go, it depends on your deadlines and budget, since option 1 is a cheaper and faster way in the short term, and option 2 is a cheaper and faster way in long term. The way I see it is that by not providing the same templates for mobile and desktop and tablet users, you will secure someone to provide the best experience for all users.
This is truly a solution for your project managers.
UPDATE - based on comments
In this case, I would go on to develop a separate mobile application. I would even think about using alternative technologies for streaming updated data in real time. There is a good comparison between Rails Live Streaming and Node.js.
If you decide to introduce new technologies or not by providing a separate application for mobile users, you will provide maximum mobility and be able to fully concentrate on this.
I don’t see different domain names being too much of an SEO issue. You should be able to take advantage of the existing visibility from the main site and with a separate domain for mobile devices, you can significantly increase the ranking of your SEO without doing any additional advertising.
I assume that you yourself have come to your own conclusions regarding the best way forward, and the best advice I can give you is to tell you to just give yourself a little more time to think and let your chosen decision strengthen and I’m sure that if he is right, he will simply “feel” the right to you.
Nobody knows your business better than you, and it is really impossible, without participating in the project and business, to say what is ultimately the best option.