That existing 4' high loop is really delving into a rather gray area of the code. Normally the trap is considered the official point of transition between an appliance drain line and the house DWV system and in that case the manufacturer of the appliance may determine the required diameter of the appliance drain line which is determined by the volume and velocity of the discharge from the appliance. Generally the manufacturer will print a table in the installation guide that defines the size, length and permissible vertical lift of the drain line with recommendations to increase the line size if you need to exceed the length or vertical lift. That table will also define a maximum length or lift which is determined by the output pressure of the pump in relation to pipe friction loss or maximum vertical static head. In most cases the code will require that the appliance drain must be in an accessible location to permit servicing in the event that line should become obstructed. Whenever a drain line is permanently installed in the wall it is then classified as a portion of the structure DWV system and it would require that there must be a trap at the beginning of the concealed section of the line and the minimum permissible diamter of the line would then be determined by the DFU (drainage fixture unit) load value of the appliance or fixture being served by that drain. In the case of a dishwasher the DFU load is 2DFU's which would require a minimum of an 1-1/2" drain line. The plumbing codes also require that a dishwasher, washing machine, HVAC unit or a home water treatment discharge line must also be connected by means of an "indirect waste receptor". Under some local codes you could achieve the indirect waste receptor by installing an "Air Gap" or they may require you to install a standpipe on the trap and connect the dishwasher drain to a standpipe in the same manner as a washing machine line is commonly connected to a standpipe. (Some codes require all dishwashers to have an air gap, regardless of how the drain is connected. Check your local code.) Under the UPC whenever we have two common vented gravity flow drains connecting to the same vertical riser we are required to use a "Back to Back Tee" (4-way) however code prohibits connecting two commonly vented drains by means of a Back-to-back if one of those drains is receiving the discharge from a powered drain I.E. a dishwasher or washing machine. The discharge from a powered drain is required to be connected by means of a directional fitting (baffled Tee) and generally the baffled tee should be placed lower than the gravity drain. In your case the simple solution would be to connect the dishwasher to the disposal input port, providing that is permitted by your local code as well. (For reasons known only to the AHJ some codes prohibit connecting a dishwasher to a disposal input port..One code that immediately comes to mind here is the Illinois State Code.) Your screen name is Tom-in-Seattle so I am assuming that you are actually in Seattle. I am not certain but i believe your code is modelled after the UPC (Uniform Plumbing Code). If so the defined trap and waste arm size for a kitchen sink is 1-1/2" but under the UPC all vertical risers and drain lines serving a kitchen drain must be a minimum of 2" pipe. You may use an 1-1/2" pipe for the vent. There is some question about whether the length of the horizontal offset on the vent in your attic would pass, but I doubt that it would even come into play unless you happen upon a hardnose inspector that is really intent on finding a problem.

Having gone through the cancer arcade myself, I relate to your concerns. Your oncologist should be able to determine from a CBC whether you're neutropenic or otherwise immunocompromised. The longer the time from chemo/rad, the better your odds, assuming one is otherwise healthy. The actual job should not involve large quantities of gray water, only the trap contents, at most a pint. Careful work = no spills. Cast iron cutting swarf is very heavy and will likely stick to the plastic. In short, don't worry so much. Although the innards of kichen drains can be disgusting, very few, if any, plumbers suffer from working on them or blackwater piping. You're not doing the work, right? Any glop that's spilled gets aerobic in short order and presents minimal hazard. Dosing with bleach seems overkill. You can ask the plumber to remove the waste materials, not an unusual request. There may be a fee.

It's a relatively simple plumbing job that's done in virtually every kitchen redo that happens. The going rate around here is around $300, with no drywall repair, plus the install of the disposal, which adds another $100. Your area may be more costly as prices are geographically based. Newer sinks are much deeper, and then you add in the depth of the counter to undermount them, plus a disposal, and even with the compact disposals most plumbing systems require that to have enough fall to drain properly. It's really not a big deal to do. BTW, it's the height of all of that above the waste arm that's the most important measurement. And since the height of the waste arm hasn't been mentioned, there is no way to know if changing models will actually satisfy the fall needed or if you would still need to lower the waste arm as is typical.

The ASTM regulations do state as lazypup says. When you are having new work done, you have every right to expect the work to be done properly and professionally. Your plumber knew to do everything 100% by the book. It's not baloney. The OP didn't question if this was to code. The OP wanted to know if it would hold in accordance with it's use and, it will if completely glued. I think the plumbers experienced assessment of the issue at hand determined he could save you some money and resolve the problem. An experienced plumber knows the characteristics of the materials he uses as well as the integrity of the configuration of the installation. This knowledge allows him to exercise a bit of discretion on specific issues. But I think you can be assured, if the joint was thoroughly glued, it won't come apart, for the reasons I stated. You have every right to push the issue and have the plumber return and redo the work. Of course, it will require additional supplies and additional charges for only that portion of the work. Of course, you shouldn't expect to pay him to undo whatever you are not satisfied with.