I understand it's frustrating to have a name you love and can't use, I've felt the same (and came to realize nothing could replace the real deal, so I picked something else instead).
Anyway, according to the baby name website I looked at :
The name Matilda is used to a great extent; it has 51 derivatives that are used in English and other languages. English derivatives of Matilda include Mahault, Maiti, Maitilda, Maitilde, Maltilda, Maltilde, Mathilda (used in German too), Matia, Matie, Matti, Mattilda, Matyidy, Matyld, Maud, Maude, Metilda, Metilde, Tildie, and Tildy. Other English variants include the contracted forms Mat and Tilda (used in German, Scandinavian, and Spanish too), and the familiar forms Mattie, Matty (used in German too), Pattie, Patty (used in German too), Tillie, and Tilly (used in German too).
Derivatives used in other languages include Machteld (Dutch), Macia (Polish), Maddy (German), Mafalda (Italian, Portuguese, and Spanish), Mahaut (French), Mala (Polish), Malkin (German), Mallt (Welsh), Matelda (Italian), Mathild (Hungarian), Mathilde (French, German, Portuguese, and Spanish), Mati (Spanish), Matild (Armenian), Matilde (French, German, Portuguese, and Spanish), Matusha (Spanish), Matylda (Czech and Polish), Mechthild (German), Mechtilde (German), Metta (German), Mette (German), Thilde (German), Tila (Polish), Tilde (German, Scandinavian, and Spanish), and Tylda (Czech).
So maybe you can find inspiration in there (Marcia ? Mafalda ? Mahaut ?)
Or different names with similar sounds :
Marina
Margaret
Maria
Maya
Madeleine
Magdalena
Maelle
Maeve
Magalie
Marcella
Mariana
Martina
Also, think about what sounds you like in Matilda. Is it the Ma ? The -ilda ? Look at other names that have those same sounds.
For what it's worth I don't find Madison particularly awful, but I do think you may be disappointed in the long run if you use it as a replacement for Matilda.