I shouldn't think cubecart would pose too much of a problem for a shared host, at least not so much as to warrant considering VPS so soon in the game. The majority of carts are generally friendly but if you stack a heap of products in them or, in particular, resource eating plugins you'll definitely run into problems.
If you're using any plugins, disable all but the absolutely necessary ones.
In regard to the "server test" you mention that informs you that your server has "been busy for weeks", are you referring to the server test within Panel or is that info coming from somewhere else?
Maximum Cash Discount on any plan with MAXCASH