If we ignore safety, this is a $10 problem. Open up the existing NEMA 10-30 receptacle, put another one right next to it, and pigtail both receptacles off the same supply wires. And you're done.
While you're in there, notice whether there is a bare ground wire laying around, separate from the wire going to the L shaped pin.
The Safe, Legal way (cheap version)
First: those NEMA non-L 6/10/14 receptacles are too fragile for repeated plug/unplug and will soon take damage. That combines tragically with
Second: NEMA 10 is an obsolete and dangerous configuration. It does not provide a ground wire, that wire is neutral. Now, when they started grounding houses in the 1960s, NFPA said "let's require grounded 4-prong NEMA 14 sockets". The appliance industry said "no, no, that will wreck our business: how about instead, we have installers ground the chassis of the appliance to the neutral wire." NFPA said "you mean bootleg ground? That means if there's a problem with the neutral wire, the dryer's chassis will be electrified and shock the user". The industry said "yes, but a neutral failure is unlikely because dryer sockets are well protected and rarely disturbed."
Finally in 1989 NFPA required it for new construction, but for existing installs, it is grandfathered to this day. It's still dangerous.
So the very first thing we do is convert the socket to the modern 14-30. This requires retrofitting ground. If there is already a ground wire in the box, then yippee, otherwise we get some bare #10 wire and run it via any available route to:
- the service panel the dryer circuit is fed out of
- anywhere we can clamp onto a ground wire that is this size or larger
If it is just as easy to run a 10/2 or 10/3 cable back to the service panel, then do that instead. Use the ground wire and hold the other wires spare for future use.
Anyway, now you have all the wires to connect a NEMA 14-30 for your dryer. Also fit a NEMA L6-30 for your equipment, and we're going to wire that paralleled/daisy-chained off the 14-30 because it turns out that is legal. You can put as many sockets as you want on a 30A circuit, you just can't plan to overload it. The "L" (twist-lock) L6-30 connectors are rated for frequent change. 6 means it is hot-hot-ground (no neutral). If any of your tools require neutral, then use an L14-30 instead.
Change all your plugs to fit the new 6 and 14 sockets. On the dryer there will be a "bootleg strap" tying ground to neutral, get rid of that.
This scenario costs about the $70 you were looking to spend.
The safe, legal way (deluxe version): Subpanel
In this scenario, you still retrofit the ground if it's not already in the dryer box.
Remember that any subpanel needs a 30” square space for the electrician to stand directly in front of the panel. There can't be equipment or a bench there. So you cannot put the subpanel behind the dryer.
You install a junction box extension and 1" metal EMT conduit from the dryer socket to the subpanel. The metal EMT conduit carries the ground, and you need 6 wires - 2 black 2 red (any colors will do here) and 2 white. I recommend using stranded wire.
1 white and both blacks (or any color) pigtail onto the original hot-hot-neutral from the supply wires, to the main lugs of the sub panel. The other white and both reds go from a 2-pole 30A breaker back to a new NEMA 14-30 socket that goes on the junction box extension. The dryer is now provided for.
Now you add whatever circuits you need, and bring them out to NEMA 6, 14, L6 or L14 sockets as needed. The appliance manual tells you whether it really wants a 15, 20 or 30A circuit, and put the appropriate plug on the appliance, and fit the appropriate socket size to the wall. You don't need to worry about 15A or 20A sockets being fragile, so no need for L15 or L20 plugs/sockets unless you are really into that. The breaker size must match the socket size (-30 gets 30A) except that a 20A breaker can power a 15A socket.
Except the subpanel is powered by a new run of 6 AWG wire, and fused at the main panel for 60A. The old dryer cable is either deprecated, or the ground to the new panel is clamped with a spur going to the dryer for a new 14-30 socket.