I think you will need a substantial increase in your budget to go to some of the inverter units that are found on RV's and sailboats, who face this same challen

I think you will need a substantial increase in your budget to go to some of the inverter units that are found on RV's and sailboats, who face this same challenge. These units that charge while in use like you want exist, but not downmarket, and they have a relatively limited (10-15 year) lifetime, and the robust ones only appear to cater to higher loads (would appreciate anyone who knows of reliable units for smaller loads like OP is talking about). I would really like an inverter design that anticipates the wear, modularizes it, monitors it, and failsafes the wear. So when the top 5-10 items that normally wear out (capacitors, inductive components, vibration isolation material, etc.) blow, a standby automatically takes over and my house supply chain management system auto-orders a replacement.