Home owner delayed and stalled over and over to make payment for my services and made me miss the deadline. What can I do now
You can sue the owner for breach of contract in court. Honestly, with residential projects, assuming you were under contract with the owner (which it sounds like you were based on the facts you mentioned) a mechanic's lien does not really put you in much of a better position. You still need to go to court eventually to prove your case in order to prove the validity of the lien. Proving your case for breach of contract puts you in the exact same position, because with that judgment you can still foreclose on the house, if necessary.
Ohio has its courts set up based on the dollar amount of the claim (i.e. how much money the homeowner owes you). For claims less than $6,000, you can file in small claims court (think Judge Judy, where there are likely no attorneys, just two people pleading their case to a judge). Small claims is the only court in Ohio where an LLC (or other corporate entity) can represent itself.
The next level up is municipal court (also called county court in some counties). Municipal courts hear cases up to $15,000. The next level past that is common pleas court, which hears any cases where the amount at issue is $15,000 or more.
An LLC must be represented by counsel in municipal, county, or common pleas court. I hope this all helps.