Is it possible to get a case tossed out on procedural grounds without needing to post bond or show up personally in court?

You have identified a  potential defense to try, but the law does not necessarily require law enforcement to try to track you down. It is not uncommon for an arrest warrant to sit, awaiting the person to be contacted by the police for some reason.  However, 8 years is a long time. Certainly you are right that statutory speedy trial will not help you but constitutional speedy trial may be a grounds to peruse. It is likely it would be necessary to show 'prejudice' (witnesses no longer available, etc.).  Also, there is an argument,ent that 'speedy prosecution' violation could be argued.  I once had a case where the defendant was in a halfway house and the prosecution waited until he was almost down with his other sentence before arresting him.  It was a case where witnesses had moved on and could not be found etc. The judge eventually did dismiss the case. Such results are rare but could be tried. That said, it is unlikely that could be done without you being physically present by turning yourself in on the warrant to get the case moving.  During COVID times, however, many hearings are being done via video and possibly that could be used to make the process less onerous.  What county is the warrant in? What is the charge the arrest warrant alleges?  BOTH of those issues can make a big difference in how the case gets handled.