The only place that has ever refused a partial payment has been my union with my union dues. They actually sent the check back and demanded the whole amount or I would lose my job.
The creditors have all told me they wouldn’t accept lower, and some even demanded wire transfers or phone payments. One even said I couldn’t mail it to the original creditor even though I was receiving bills from both the original and the creditor they hired. All of them cashed my checks just fine. They weren’t happy, but I was paying something, and I could prove it.
I would go ahead and send what you can. Yes, it will probably go to a creditor, and just send what you can there too. None of my creditors have bothered to take any legal action, probably because my bills aren’t that large, and I do have a record of paying, just not as much as they would like. At least you can establish a record that you are hanging in there and doing your best. They don’t have to like it, but it’s better than nothing, and you already know you can’t send more than that.