Unfortunately - that is not a mater of choice.
If your would have your actual work location in OR - OR state income tax withholding is required.
If the company would employ you if Florida - they are required to register in this state and remit employment taxes to the state. Yes - there are no income tax in Florida - but there still SUTA payments. If the company doesn't have any nexus in FL - that will be additional overhead.
If your income from OR sources is less than certain amount - you do not need to file OR tax return, but the tax return is required if you are due a refund from withholding.
Your non-resident OR tax return may cost you about $100. You may want to negotiate the compensation this matter.
If your actual work location is not in Oregon or you work in multiple locations - the company should indicate your actual work location and withhold taxes for that state if needed.
I just took extract from your statement above:
I have frequently worked ...in other states ...I was not required to pay or file an income tax ...for either state.
If you are working in the state - the income is considered from sources in this state - and in general - if the state has income tax - your income is subject of such tax regardless if it is paid to you on 1099 base (self-employment contractor) or W2 base( employee).
If you inform your accountant that you worked in the specific state - he/she would tell you about such requirements.
As there is no any records where did you actually work - neither NC nor PA DOR are looking for you. Generally without knowing the situation - it looks as all work was done in your FL location.
That is my view on your situation.
For an employee - the situation is different - the company should register in the state it has employees and is obligated to pay FUTA and SUTA taxes.
They also are required to track your work locations, withhold and remit employment taxes and report that on W2 form.
There is no room to escape from state tax liability as it is in self-employment case.
Please feel free if you need any clarification either now or later.
I understand your frustration - but your demand puts additional pressure on your potential employer and they may reconsider your employment.
You may ask for additional compensation to cover state tax liability - but by asking not to report your actual work place - you are pushing them into the tax avoidance practice.