If cost is the issue, then the current setup seems best - simply have the Chief Justice of the Supreme Court carry on as the
Administrator of the Government, and stick to the essentials of non-partisan head of state duties, like assent to legislation, etc. In fact this very well could be the best set up for having an actual legal expert decide on possible constitutional responsibilities that could happen, like having to decide on proroguing Parliament. (Remember that the Supreme Court itself operates on a majority basis, so having the CJ individually as Administrator doesn't imply that the judiciary has taken over the executive.)
Other ceremonial tasks, like national honours and awards, could be stopped or delivered on a cost-recovery basis (e.g. application or nomination fees, sponsors, etc). We would retain the existing set up with Queen Elizabeth II and heirs as official head of state to avoid the costs of legal changes, changes to symbols, ranks on uniforms, a selection process for a head of state, etc. but curtail any visits and associated spending.
If the issue is having a head of state other than one who is also a head of state of other countries and not living in Canada, I think it would have to be balanced against the benefits of the current set up. The Queen is clearly non-partisan and no Canadian can ever say that she/heirs have a bias or political slant supporting one Canadian group or another. And even if she/heirs did, being non-resident it would not be of any effect day-to-day. I don't think there could be a Canadian, that would be ever above any perception that they could have some bias or be subject to popular pressure in the same way the Queen/heirs are. No one will ever ask the Queen her stance on a Canadian political issue, nor will the Queen ever have an inclination to respond or have something in her past that would imply taking sides and leading to intervention or pressure on our government. Any kind of election or selection of a Canadian opens that door to politicisation; at least with the Queen/heirs as head of state, no one can ever finagle or machinate their way to the role.