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Digital electronic thermostat will not necessarily solve your problem, I will be happy to work with you on this but perhaps first we should investigate the current situation.
it is quite likely that the DIFFERENTIAL setting on your current thermostat is simply set too wide... are you aware of that setting.
Also tell me if the current thermostat has a coil of thick tubing attached to it, or if it has a sensing bulb attached to a long thin copper tube.
The location of the thermostat and its sensing element is also very important.
(precise temperature control, within 1/10 deg F had been one of my specialties before I retired)... in your case we can achieve + or 2 degrees F cost effectively with a mechanical line voltage thermostat.
Digital line voltage gets very hard to find very expensive and will generally not perform any better than a well placed properly selected mechanical thermostat.
We can go from there.