Hiring property manager

This will depend on your State laws and Associations governing documents.

What is the reasons people give for not wanting to fill those positions?
It's possible that it's just too much work. You may want to look into hiring a bookkeeper vs. a property manager to collect the mail, maintain accounts for individual lots (tracking payments) and make bank deposits. The Treasurer would then be responsible to keep the check book, pay bills and help prepare the budget and financial reports.

Personally, I do not believe in giving control of the check book (treasurers duty) along with collecting and depositing money to someone who isn't a Director. It's like giving your personal checkbook, savings account and paycheck to someone standing on the corner. They might be bonded and capable of doing the job but how soundly would you sleep at night? I believe it's ok to split the duties (hence the suggestion of a book keeper). Anyone can make deposits, but I wouldn't give them complete financial control.

However, if you do think turning over your personal finances to a stranger is a good idea, send you next paycheck to me.

We use an independent contractor who is a member of the community to provide book keeping services. Costs us $350 per month. Note that I said independent contractor. Hiring someone as an employee would require the Association to pick up additional expenses as an employer. Hiring an independent contractor does not make the Association an employer. Here is a link to the IRS web page Independent Contractor (Self-Employed) or Employee?

Do your governing documents require a Director to fill any of the offices?

Some HOA bylaws require only that the positions of President and Vice President be board members and/or homeowners. The positions of secretary and treasurer may not need to be board members nor perhaps even homeowners. Some bylaws also allow the board to appoint an assistant secretary and an assistant treasurer. First, see what your bylaws require and what they allow. Then, you will know what your options are.

Personally, I think the treasurer should be a homeowner and a board member. But, if you appoint an assistant treasurer to do the day-to-day activities, prepare the budget and financial reports, etc., the treasurer's role then becomes one of signing the checks and reviewing and approving the budget and financial reports prepared by the assistant treasurer and presenting them to the board.

Sometimes it is helpful to find a volunteer to be assistant secretary. That person attends board meetings, takes notes, prepares the minutes, and submits them to the secretary for review and approval. The secretary then reads the minutes to the board.

Keep in mind that officers (and assistants) who are not board members have no vote at board meetings and cannot participate in debate or discussions. They may answer questions and offer advice only when asked.