My kids don't go to Montessori schools, but I do incorporate some ideas in to our home. First thing, I would rethink the limited toy thing. Kids this age have a short attention span(2-10 minutes). You need enough for them to be able to rotate through toys. I would try things like Duplo, matchbox cars, little people, plastic dinosaurs/animals, balls, simple dress ups (daddy's shoes/tie), play food/dishes, pegs and peg boards.......
Allow him to help you around the house. Let him do simple things like stir whatever you are cooking (all my toddlers stood on chairs just fine), give him a damp rag to "clean" with, have him help put away laundry/fold laundry (wash cloths, match socks, etc.). I think you would be surprised about how neat kids can be when they are taught to be. I mean they are small they will spill things, etc. But it is not that difficult to teach them how to properly handle kitchen items. Give them very simple jobs to start with.
I set up a small shelf when my youngest was about 20ish months old. I put out 3-5 different activities a day. She could choose to do them or not. It worked well in our small space. I would open and close the shelf (covered with a piece of fabric) so it kept the toys special.
Some simple fairly neat and quiet activities are
-Build blanket forts
-make a basket ball game out of rolled up socks and a laundry basket
-pretend to be different animals
-Bath tub painting
-long baths lol
-dropping milk caps in a hole in the top of a coffee can (seriously my toddlers loved that lol)
-make different shakers out of water bottles, rice in one, beans in one, water in one, etc. Glue to the tops on
-sticking spaghetti noodles in a spice jar
-simple transfer activities (I used pompoms, "jewels", beans) 2 bowls and 1 spoon.
-collages (use a glue stick and it's not very messy)
-pouring activities( I started with a small amount of beans/rice in a small pitcher and one cup to pour into.)
-let him play in the sink and "wash" dishes.
-magnets w/magnetic and non magnetic items (make sure they aren't small enough to eat!)
For messier things throw down an old shower curtain to protect the floor or do your projects in the kitchen. Teach him to walk to the bathroom with hands in the air when he is messy. Some "cleaner"(as in they won't stain lol) sensory ideas are grass seed, oats, noodles, rice, lentils, beans. Also I found 18mth-3ish to be more demanding ages all around. Around 2.5-3ish my kids all started playing much better by themselves and for much longer periods. :)