There is no excuses, if there is a will there is a way, you can pray anywhere, I used to pray in a dirty storage room back in those days when I was starting out or in the office in a corner, sometimes at the very spot were I sit (putting the chair to a side)
I remember praying at a stairwell in a library at university were 99% were gaalo and a group came past thinking I was praying to Jesus, these are all public displays of Dawah along with your good character.
The reason you refuse is because you feel ashamed, and you feel ashamed because of a lack of iman, and that lack of iman is as a result of your distance from Allah.
I remember when I was very young my Grandma would pray in a park when salah time came in front of all the Gaalo who would all stare at her (20 years ago), back then I used to feel ashamed while at the same time in awe of her immense courage, she of course didn't give a damn about these people.
I understand that societal conditioning is very powerful, but you need to resist this, what you are doing by combining all the prayers at home is simply not allowed, if there is a will, there is a way, work on strengthening your iman.