First everything you are talking about doing is very much in the grey area of the law. Technically it is illegal for you to add any form of antenna or connect any other device. The loophole is it is allowed if the licensee ( ie the cell) company allows it. But no cell company will actual give you any paper work because they have now assumed any liability for interference you cause.
First do not use any for of electronic "booster". Most you can get are not FCC approved so you never really know if they do what they say. The ones that are FCC approved are only sold to people who have a license...ie the cell companies again.
The antenna if you get one tune to the proper cell frequencies for the tower you want might work. The problem you have in your case is the huge amount of cable you will need. The cable is extremely expensive for cable that will not lose more signal that the antenna adds.
Do you have internet in your house. It is almost a scam but you can get what is called a micro cell. This creates a mini cell tower in your house just for you and connect to the cell company with a vpn over your internet. The scam part is they use your internet to provide the service but still count phone minutes and data usage against your cell plan. Obvisouly you should use wifi and not cell data in the house. Some vendors will actually give you a mircocell if you talk to them about poor coverage. They are not extremely expensive around $150 for most and most have no activation or monthly fee.