Folks will need to know where you are (nearest big city) to try and make appropriate suggestions.

In a word - no. Because all trees drop something and all trees take many years to size up. However if you are talking about Magnolia grandiflora those do have the particular aspect of continuously dropping individual spent parts here and there for months. With other broadleaf evergreen trees being similar in this respect. So you could change the litter situation by planting a deciduous tree. A kind like a seedless (male) maple selection where you mostly have a big dump of leaves each fall and then that is it.

Regarding the starting over issue again you are going to have to wait for the replacement to get as big as the magnolia was before the same amount of shade will be produced.

we need a pic after removal to give the best ideas ..

as well as the noted big city location ..

but its a no brainier that you do NOT want anything fast growing ... fast to get to the size you want.. fast to being twice as large ...

treees are trees.. they never stop growing ...

smaller trees still have annual growth .. but its lesser than the others ... so its take them longer to get to the size you want .. real catch 22 ...

beyond that.. i need a pic or 2 to provide ideas ..

ken