Look, as a collector of vintage linens  as my mother was I can tell you the biggest deal is to grab rust stained items for norhing or as much as 1€ at flea markets and during time I have experienced my method to bring them to life again, really simple, , smal spots of rust usually get clean with an hot wash 140f in the filter flo with good detergent, or soap with addition of percarbonate, perborate, , blood always comes out, no matter how old or dry it is, never had a problem...
But I could grab splendid bed sheets and table clothes where rust totally became part of the fabric and you could feel the hardness of the iron to be stuck in the clothing, they usually comes out with alos as iron became part of clothing..
I treat them like this:
To weaken  the extra rust  I do a wash with plenty of detergent 3-4 scoops in hot water 140f ( my water supply reach 150f).... I do stop  machine for an overnight soak...
Let it compete cycle the next day...
Get it out the washer, check that it is enough weakened, start machine again and as soon as the washer filled I treat the stain with a specific product for rust called "rapida" togliruggine (italian product) and toss in the washer quickly.... It's the best product I could use...
It is fluoridric acid   and if it sits too long it will weaken the clothing, but it is a kind of product that somehow is safe to be used on colors and does not  damage them if you make sure you immediately toss the clothing in the machine with water in the first minutes.... Not any damage or weakening of the treated point....
I brought to life  again linens ane clothes that most of commercials  laundries my friends or relatives  could bring them to, renounced to get clean.....
Another stain that most friends  bring to me is mold, I succed in removing it just fine with an hot wash, nothing more,  thing that with my big surprise says they cannot manage to do..... This obviously when it is not so much attached badly and turned to be all the fiber to be mold...then you cannot do anything, well mold goes away but you  get an hole where first you had mold....as it is washed away like dirt is...
All this to say that if really you cannot get it  away with a wash, you may try the fluoridric product....I attach a link, can send you some if you want...it fits in an envelope, it should not cost much to ship, but I bet in the US you can find equivalent stuff....