A heat pump is actually an air conditioner that has a reversing valve which allows the refrigerant flow to reverse so that you pick up heat from the outside air and with refrigerant you take the heat in to the indoor air coil. The heat is then removed as the fan blows air across the coil. Most heat pumps have some sort of backup "emergency" electric heat for use during the defrost mode or when there is a problem. If your unit is in fact a heat pump this electric emergency heat is probably what you have been using to heat the home. One of several things could be wrong. You could have a bad thermostat, bad mode switch or of the unit is fairly new or manufactured in the last 15 years or so it probably has a control board that manages all the functions including the defrost and there could be a problem with it. Any of the above functions I would recommend you repair the unit rather than replace it as it will be much tons cheaper to repair rather than replace. If there is a problem with the compressor it isn't necessarily any cheaper but a lot wiser to replace the unit rather than repair because of the warranty the new unit will have. In the long run you will save money. Did they tell you what the problem was or just tell you that the unit needed replaced? If the unit does in fact need to be replaced a cheaper alternative to the heat pump is a air conditioner with electric heat. This typically costs half to two thirds the cost of a heat pump. It isn't near as efficient and will cost you more to heat the house than a heat pump but the upfront costs are considerably cheaper. Hope this helps and good luck!
Also, have you thought about just installing a typical ducted system rather than have a hodge podge of window shakers and portable units? The portable units you have linked still need to circulate outside air that's why they come with 71" hoses. The portable units are primarily designed for short term use. By the time you install a new window shaker and buy a couple portable units you will be near the cost of a typical ducted system or multi-evaporator non-ducted system like you see
here. There are several manufacturers of ductless systems I just pulled up the Sanyo site because it has a pretty good overview of some viable alternatives I would be considering rather than the hodge podge of shakers and portables.