Well to provide my update after two stays with a young kid:

• I'd tried the JW Marriott first for 3 days as it seemed the most child friendly. In some ways this was right - the staff were excellent and friendly, and we got a connecting room. However, and depending on your perspective, the lounge only allows children between 9am - 5pm, as a result with kids you get a breakfast for free in the normal restaurant... but at the cost of not being able to spend anytime there whilst there is cocktail hour. There wasn't that much to do in the nearby area for kids, but we walked to EatiThai nearby for some "safe" street food.
• On our return we stopped for a night at the Bangkok Marriott Marquis Queen's Park. What I hadn't realised in my prior stay is that it is directly attached to a nice park (Benchasiri) with a custom entrance, with two children's playgrounds and other things to do. The lounge allowed children at any time and was superior to the JW in terms of selection of food (lower quality though). What was less fun was that check-in was very slow (especially considering they knew exactly when I was arriving) and even at 5pm we couldn't get connecting rooms or even rooms on the same floor and we were in the North Tower when the South Tower had the lounge... however one of the rooms was upgraded to a nice M suite that had been pre-prepared with a welcome gift, including little toy for the kid

Next time we'll likely return to the Queens Park Marriott, though our overall time in Bangkok was rather spoiled by the awful traffic for both hotels after about 11am, which made it so hard to get around except by foot.