Unfortunately, I think you are going to be faced with a different experience of many of the sites on the Tokyo part of your itinerary than you are expecting. If your kid is already used to prams/strollers it’s hard to imagine s/he adjusting to something different on top of the new surroundings and weather.
As well as the usual difficulties with managing all the long, long gravel paths leading up to Meiji Jingu, other places such as Chidorigafuchi, Harajuku and Yoyogi Park, Sensoji Temple and Ueno Park would all be just about manageable with a child carrier but stressful and frustrating with a stroller. The reason is that all the children and students are on holiday during the last two weeks of March so “young” areas (like Harajuku & Tokyo Dome City) are ram packed and when you combine this with Sakura peeping hotspots that are in bloom, like Chidorigafuchi and Ueno Park are likely to be, the crowds are overwhelming. Sensoji is crammed at the best of times, Nakameguro is a “young” area AND has Sakura enthusiasts. For a lot of your plans, late March with a stroller will be a challenge.
Remember also that the stroller will make parts of the Koishikawa Botanical gardens a little tricky, but between two of you, managing a few pond/lake stepping stones shouldn’t be too difficult. There will probably be alternative routes here though. This park shouldn’t get too busy.

So long as you are at Tokyo Disney for the evening atmosphere rather than to ride on anything you might be OK, because, late March, typical queuing times are between 2 and 3 hours long. Don’t set your sights on having a picture with Mickey unless you want to spend your whole time waiting in line for the privilege. Late March is NOT a good time to go to the Disney Parks. Not that it’s an ideal time either, but the evening of Saturday the 5th April might be slightly less packed.

Saying all that, it is very easy to avoid crowds in Tokyo in late March. For example, you could go see the sakura at Showa Kinen Koen out in Tachikawa, or spend some blissful hours at the Nihon Minka En* (the baby can crawl around inside the buildings there and play with sticks and stones in the dirt outside, heaven!).

* If you do look into Nihon Minka En, worth noting that it is part of Ikuta Ryokuchi park which has some celebrated sakura viewing areas. These are highly unlikely to be blighted by crowds. https://japantravel.navitime.com/en/...11-sak1307076/
This page provides a virtual visit of the main viewing spots on Masugata Hill: https://tamaplaza.news/170410_masugata_hill