I suggest you contacting the operator directly on what to do and if they have any interim solutions or not.
Afaik, Singapore uses both 900MHz and 2100MHz network for 3G, where the 900MHz network is for coverage and 2100MHz is for capacity.
Very likely the network you're latching on when you have service at home is the 900MHz network.
Therefore, with 2100MHz may not be available inside your home and putting this kind of repeater is useless.
For example, M1 have the HomeCell Coverage solution, where there's a 3G FemtoCell loan to you to enhance network coverage around the house. It's heavily secured so you have to call in to M1 to add/remove the registered numbers, if not they won't get service from the femtocell.
I'm not sure for SingTel and StarHub. For my experience, I tried to ask for any solutions on SingTel Mobile but they indirectly blamed me for living too close to the border of the country and isn't offering any help, like wtf?
Btw, Circles.Life and MyRepublic are MVNOs, they can't offer coverage help because it's dependent on the MNOs (SingTel/M1/StarHub/TPG).
For 4G, the frequencies used locally may be incompatible, so I won't say much on that.
SingTel: FDD-LTE 900/1800/2600MHz
M1: FDD-LTE 1800/2600MHz
StarHub: FDD-LTE 1800/2600MHz
In the future, these bands may be added to the list above.
SingTel: FDD-LTE 700MHz, TDD-LTE 2300/2500MHz
M1: FDD-LTE 700MHz
StarHub: FDD-LTE 700MHz, TDD-LTE 2300MHz
TPG: FDD-LTE 900MHz, TDD-LTE 2300MHz
Afaik, there's no femtocell for 4G for now, as the VoLTE (4G Voice) devices are limited to selected high end phones from Apple / Samsung / Sony / ASUS / LG.