Hi JS. Are you located in Australia? The reason I ask is because the Expobar Office Pulser is called the Office Semi Automatic here and has a RRP over your budget.
As far as I know there are no E61/HX machines within your budget.
The Nuova Simonelli Oscar is within your budget but is not an E61. The soon-to-be-released Breville is a double boiler but may also be worth your consideration.
A machine certainly doesnt need to have an E61 group to be temperature stable, in fact there are some poor performing E61 machines. There is more to temperature stability than 9lbs of chrome-plate brass.