I do not see any problems with this solution , excepted that I would foresee some flow control mechanism on each outlet , to be able to divide the hopper gravity flow into three separate inequal flow streams , each one being calibrated to the needed filling rate capacity of their respective system.
See , a good bigbag filling system needs a high flow rate for a short period (10t/h or much more) , having then a large time lapse without any flow required , because the full BB has to be removed and a new empty BB installed manually , taking 'lots' of idle time that can be used to fill up other packaging with less high flow rate demands.
This require a short time span / high BB flow rate feed , that may not apply to your other filling machines.
I would analyse the three required flow rates , choose the required valve outlet that goes with each system and build a screw conveyor under the one that shall feed the BB installation. This allows you then to place your new BB installation somewhere else , out of the way of your current operating systems. And just have a short operational shutdown to install the new three way valve system and screw conveyor inbetween your existing hopper and the new BB installation , before restarting everything.
Keep in mind that screws usually are not longer than 10meter/30feet , and if you want to go further , a row of similar screws will be required , that are feeding each other in row till they reach the BB installation.
I had a client in the past with a similar problem. We kept it simple. Each system was fed sequentially , the sequence being decided in flow rate requirements. When the BB needed feeding , the other small bags systems were allowed to finish their current filling operation , then their valves were shut down during the 20 sec BB filling operation , and released again for operation after the filling cyclus of the BB. This was required , simply because the hopper outlet feeding couldn't cope with such a high flow rate for the three systems simultaneously. The client wanted it that way , because BB's were his main product line. We could have fed the three lines simultaneously , but the available flow rate for the BB would have been much lower , requiring a 4 minutes BB fill up period , instead of the 20sec. That was not acceptable for the client.
I guess you will have to decide your own priorities , but your problem is certainly not a big issue mechanically speaking.
If you change regularly from hopper recipe , then you also will have to take into account that the BB screw feeder will always have a residue of the previous recipe on the bottom of the screw tube. Simply because there is always a small gap between the archimedes screw and the surrounding tube body , to allow for mechanical tolerance. Most companies simply solve the issue by flushing the screw with the new recipe , and fill e.g. a half BB with the mix up recipe before really starting the batch sequence of the new recipe. That generates wastes that you didn't have previously , and you have to get rid of them , which cost monies. I don't think you will be able to avoid this , not having space under your hopper to directly place the BB system under it. Someone with lots of small batch runs and therefore lots of wastes used this product residue , which had a high calorific value, as a fuel to heat up a furnace and recycle it into CO2 going though the stack and lots of heat for their process installations.
If this is really a problem , then a way out is a vibrating table system for your product conveying toward your BB system , because you then don't have residues. I don't have much expertise with those systems , but I know that you are even able to let your product climb up on a vibrating downward hill ramp , when applying the right vibrating frequency. This can be an option for you , if you can't accept the waste problem going with a screw conveyor. Although vibrating table conveying systems are major noise making devices , and lots of people are reluctant to use them simply for this issue.
Another possibility is to place a rotating valve system underneath your third outlet (doesn't require lots of height) , install a dense phase conveying system blowing the powder falling from that rotary valve to the BB installation. Advantages : you can go 100's of meters/yards without 'any' problem. Disadvantages : much lower flow feed rate than with a screw system + compressed air requirement that are not minimal , this air being used as a piston to blow props of products toward your BB receiving installation. Other possible disadvantages : static electricity build up and bridge forming above the rotating valve due to blowby leak air from underneath the RV , leading to installation shutdowns. Transport pipe clogging , requiring emptying of the whole blow pipe routing because of product in them that can't be blown away anymore , is also a hazard.
You have a variety of solutions for your problem , but the specifics are in your hand. If the hopper recipe doesn't change , go for screw conveying. Simple , rustic , maintenance friendly, clean. If the recipe changes sometimes , go for screw conveying. If the recipe changes every shift , go for pneumatic transport , and demand steel hard work guaranty for the products you want to transport.