Turkey took 2 hours longer in oven with no bottom element

I suspect that your oven has a hidden bottom element as I've never seen an electric oven w/o a bottom element.

Regardless, in a working oven the whole oven should be near the desired temperature. It will be a lot closer to even throughout the oven if you have a convection oven.

Since the oven took much longer than expected here are a couple reasons that could affect the temperature and/or cooking time.

1. Was the turkey completely thawed? A turkey that isn't thawed takes a lot longer to cook. And don't think that fresh turkeys are ready to pop into the oven. They can be cooled to 28F (I believe) and still be called fresh. They aren't frozen solid but they aren't ready to cook as is.
2. Check your oven with an oven thermometer. Ideally you use an oven thermometer every time you cook but certainly use one until you understand how accurate your even is calibrated. And then every few months afterward. You might find out that setting the dial to 350F gives you an oven at 300F.

I remember using a pan that was too big for the oven (it covered almost all of the rack) and burning the bottom of the dish. The heat couldn't reach the thermostat so the lower element never turned off. Not what you were experiencing but shows what can happen in non-convection ovens.

If you can provide more information (make & model), which rack position the turkey was on in the oven and the size of the turkey, you may get a better answer.

There is nothing wrong here. Formulas by weight are just very unreliable, and you stumbled over one of the more obvious cases. You just have to cook until everything is done, no matter what the clock says.

If you suspect the oven is baking wrong, use a thermometer to find out how much off it is, with and without something in it, and if you find it to have a very large gap between the indicator and the actual temperature, you may choose to change the dial setting in future. But you will have to make several measurements at several settings - if you were to find out that it heats to 135 Celsius when set to 175, for example, this is no guarantee that it will heat to 175 when set to 215.

When it comes to planning, you might want to write down values from your own experience, as they will be more reliable within your kitchen than generic rules. Also, try using formulas developed for whole birds - the ones which are meant for small pieces of meat are approximately accurate in the range for which they were developed, and have a very large error when scaled up.

Answers you have are on point, the temp of the oven is the temp regardless of if there is one element or 10. It really only makes a difference for nearness to the element which might give you localized heat or some browning effects for open elements. Especially if it is a new oven though, get a thermometer and check you settings for accuracy. One question I would have though is are you sure the turkey was fully thawed? If still partially frozen it could greatly effect the cooking time.

With turkeys, I have raised my own in the past that were allowed to free range, were older than the average commercial turkey and did not have water added. Those birds typically would take a good 30-60% longer to cook for the same size because of much denser meat than your average bird that has 10% or more injected salt-water. Double the time is pretty extreme but range can be very substantial just from how the bird was raised.

Stuffing a bird as opposed to not can easily add 25% cooking time or more. Another variable I have experienced, was the cooking cavity of your previous oven smaller than your new one? I have found that smaller ovens for me have cooked large items like turkeys much faster, but also less evenly, than a larger oven because the smaller cavity results in more indirect heating. Less even because it has poorer circulation so the heat is not as even.

Just tossing a few variables out that can and sometimes does effect things. Temperature would usually be the most common issue though and is is always good to verify temperature on a new oven, and at least periodically on all ovens.