Each employer should specify what they will pay for, or if there is a maximum amount. they will pay. An employer might even give a flat amount no matter what your expenses.
Before the 2018 tax changes it was very import to be able to document your expenses, and submit it to the company. If you followed the riles set forth by the company, and they followed the riles from the IRS, then your reimbursed expenses were not taxable income.
But under the current tax law you can't deduct your moving expenses, and if the company pays for your moving expenses it is taxable income.
So this boils down to following the rules of the companies. Avoid submitting the same expense to both companies. If caught they can decide that you filed a fraudulent expense report and at the least want their money back, and at the worst they could fire you and want all the moving expenses back.
Please review what expenses they cover. Do they pay for a moving company to load everything and drive it to the new place? what happens if you do it yourself but make multiple trips? What about mileage and hotel? I know Boston to NYC doesn't require a hotel, some some moves involve hotels and/or airfare. If the extra trip to Boston was to do something unrelated to the moving process, neither company may consider it an allowable expense.
Now if both companies have a maximum amount, then see what can be logically split so that you stay under the company maximum. You could put all the mileage and tolls under one, or split them if you have multiple vehicles that have to be moved/relocated.
It can be more confusing for the employer if you try and split a single bill between the two companies, they may have trouble understanding why the amount claimed is less than the amount that appears on a receipt. That confusion can slow down reimbursement. It can also lead to trouble if the accounting department corrects the "mistake" and gives you the extra money.