I think those logs that supposedly embrittle tar rely on a slow cool burn which condenses sulphur on the inside of the chimney, it then takes weeks to work and you can't use the fire during that period because it'll vaporise (or worse, burn) the sulphur off. I don't know how a smokeless fuel would help (other than by not adding to the deposits) as they are very low in sulphur.
Stoves with secondary burn do a good job of destroying the tarry compounds in smoke, but work best when running flat out... if the stove is turned down to reduce output, the temperature of the hot air for the secondary burn can get too low. This doesn't matter so much with logs as they cook through fairly quickly, driving off the volatile stuff that causes the problem in the chimney... so if you turn the fire down once the room's up to temperature most of what's left is charcoal which doesn't produce much smoke. Sawdust blocks are less good at conducting heat to the inside so tend to produce creosotes continuously as they burn: turn the stove down, the secondary burn gets inefficient and the nasties can condense in the flue.
I'd ignore the tar until next summer and then try the chemical logs followed by sweeping. Then fit an insulated liner... it keeps the smoke hot and gets it out faster.
In the meantime a flue thermometer may help your parents keep the stove exhaust at the optimum temperature.
Mind you, a chimney fire does an effective job of removing tar... as a neighbour of mine discovered a couple of years back. The plaster explodes off the walls too.