From your description, it sounds very much like you're living with plaster and lath walls. If I'm correct, there are two possibilities for solid fastening.
Find the studs. They are probably 16" apart, so once you find a couple, you can probably find more. Stud finders in those walls are fraught, as there's so much wood and metal to confuse things. If you already have holes, you can stick a bent clothes hanger in and spin it to find a stud. (Unless, ha ha, you have insulation in the way. Then all bets are off.)
Get a picture rail high around the perimeter and hang the art from it wherever you want. You still have to find studs, but at least it's a one-off exercise. Plus, it's very much in keeping with the 1904 aesthetic.
Edit to discuss stud finding…
- electrical boxes and switches usually have a stud to the immediate left or right of the junction box. This, plus knowledge that studs are usually 16” center to center can help.
- if there’s no insulation, and you already have a small (like, 1/4”) hole, you can bend a coat hanger into a square U shape (~9” legs). Stick one leg of the U into the hole and spin until you tap the stud. The visible leg shows you where the invisible leg is hitting the stud. Spin the other way and you might hit the other stud for verification.