Your question does not have simple answers have you used a watt meter to see the current your motor is drawing at full throttle? With any installation its a good idea to do that test since its a good way to match motor and prop.

LiPo batteries have a better current delivery than lead acid BUT you do need to be careful about end voltages so as not to damage the battery. Many ESC have a voltage cut off built in to protect LiPo batteries it may be your hitting that limit with your lead acid battery.

The simplest solution to your problem is to look at the Amp/hour rating of your existing battery and get something with a higher rating. Going LiPo can give a much higher rating with a LOT less weight. The downside being the need for a special charger and the need to be careful about storage and end point voltages.

As to putting 2 batteries in series to get a higher voltage yes you can BUT increasing the voltage to a brushless motor requires you match the prop to the new voltage running on the existing prop will probably cook the motor. How hot is your brushless running now? Outrunners generally can swing a bigger prop than inrunners.

Hi, Lead acid doesn't like delivering the high currents brushless motors want. They are more suited to long term low currents.
Go for a LiPo, 3 or 4S, something 7AH plus should keep you going for a while. Don't put batteries in parallel as one will inevitably try to charge the other, unless you have a hi power diode board in between them to prevent that. Cheers, Doug 😎