FilteringEnabled: How do I get past the server changing values for a particular client?

Introduction

So, I'm experimenting with FilteringEnabled, and I need some things to replicate to the other players for my vehicles to work properly (Sounds, Motors, stuff like that). I have a local script under the vehicle that detects changes (using the .Changed event) and sends the values to the server via RemoteEvent, which sets the values so everyone can see them.

The Problem

Since the server is also setting values that the driver is setting, there's a little jitter between when the client sets values and when the server sets them. This is most noticeable when setting a value quickly and incrementally.

Example

From the client to the server

--"Val" is a value being monitored for changes
--"Server" is a folder containing the RemoteEvent
Val.Changed:connect(function(p)
local newValue=Val[p]
Server.RemoteEvent:FireServer(Val,p,newValue)
end)

...And the server can now replicate the value(s)

--"Server" is a folder containing the RemoteEvent
Server.RemoteEvent.OnFireServer:connect(function(Player,Object,ValueName,Value)
Object[ValueName]=Value
end)

One way to avoid this is to have the Server use :FireClient() on all the client except the one controlling the vehicle, but this requires the values to go from one client to the server and then to all the clients. This also means that a new player joining the server won't see the value replications that took place earlier before. I'm trying to avoid doing this, even though it works. I feel like there's is a better way.

Thanks in advance.