What batteries to buy instead of 9V batteries?

Hello, here I have a question! There is a device running on a 9V Krona battery. Basically (and this is 98-99% of the device’s operating time) it consumes 1.1 mA in current. Sometimes (1-2% of the device’s operating time) there are current surges up to 50 mA. The minimum battery voltage (salt) with which my device worked was 7.15V. I decided to buy batteries, but I can not decide on the choice. I have a choice between two batteries (hereinafter referred to as battery). The first battery (Li-polymer) charges up to 9.5V. Tests have shown that at a load of 100 mA at the output of the battery, the voltage is 9.5 V and after 3 hours the battery is discharged i.e. its capacity is 300mA / h. During these 3 hours, the voltage at the battery output is stable 9.5V (only hundredths of values ​​change). The second battery (Li-ion) is already charged up to 8.4V. tests showed that at a load of 130mA the voltage gradually decreases to 7.3-7.2V in 4 hours 30min, and then drops sharply i.e. its capacity is 585mA / h. Question! What batteries should I buy so that the device works as long as possible on one battery charge?