We can't fit a full size cot in our bedroom
Have you got a chest of drawers in your bedroom? You could move the drawers into the nursery. Likewise wardrobe.
I mean the bottom line is you will either be (a) padding into another room all night for many months yet and suffer the sleep deprivation that goes with that. Or (b) end up co-sleeping out of sheer exhaustion, which you have said you don't want to do.
So finding a way to for a co-sleeper cot into your room is a simple solution all round. Baby is likely to be waking in the night for some time you, you are kidding yourself if you think otherwise so this is more about making life as easy as possible.
How do you 'ensure' frequent naps
You need to just full-on focus on it. Baby's don't 'just go to sleep' so you have to work really really hard at it. Baby not going to sleep (or not staying asleep) is not baby's choice - it is not baby saying they have had enough sleep. It's just all they can manage without more help.
I mentioned bouncy chair. These with the dummy are great for focused 'I am going to keep going until you go to sleep whether you damn well like it or not'. Baby in chair infront of you while you sit on the sofa. Then foot on chair and foot bounce. Bounce, bounce, bounce, bounce that bay into sleep oblivion. Keep putting dummy back in as needed and keep bouncing. If/when baby wakes or stirs, gentle bounces and dummy reinsert to try to lull through one sleep cycle into another to keep baby asleep.
I favour EASY to ensure regular naps and feeds in the daytime. This is a structure of repeated cycles that are repeated throughput your day. You modify the length of the cycles according to your individual baby but as an estimate I would be doing 2 hourly EASY cycles at 4 months old.
E - Eat - Start with a full feed
A - Awake Activity - Ideally about 60 mins from first waking at this age, no more than 80 mins. If it takes a long time to settle baby to sleep then activity time is reduced accordingly
S - Sleep - Bouncy chair, dummy, you sat on sofa. Foot bounce, bounce, bounce.
Y - You time - While sitting on sofa when baby sleeps.
Repeat, repeat, repeat.
If it takes you, say, 30 minutes to get baby to sleep then activity time might only be 30 minutes from waking. This includes the time take for the feed. So if a nappy change is needed it might just be 10 or 20 minutes playing the working on getting back to sleep again.
Likewise if your baby's naps are short, then you might need to shorten the whole cycle down. The key is to pay attention not to nap time, but awake time. However long baby sleeps for, aim for helping him back to sleep within 60-80 minutes of waking up.