hi,
i know you say you dont want to use ear plugs but i had similar probs in different rental houses over the years and found one particular type of earplug to literally be a godsend. otherwise i'd have gone mad from lack of sleep. they are called Quies earplugs and are available in pharmacies. they are made of wax which you roll between your fingers until soft, then insert into ears and they mould to the shape and literally block out all noise very well, you can still hear your alarm or a smoke alarm etc but outside noise is totally gone. i cant recommend them enough. it takes a week or so to get used to the sensation of them being in your ear but i guarantee they are as close as you'll get to soundproof without spending a lot of money on DIY changes to the windows/ walls etc. give them a go anyway they're only a couple of euro for a box of 10 pairs i think, so nothing to lose