(I'm sorry this is too long, it needs some editing.)
What you likely need is a single broadband antenna thats horizontally polarized. A so called fan dipole (a bunch of different band dipoles all fed in parallel- would work. But don't use a simple dipole with coax without a
balun.
From my own experience, I can tell you right now that the thing you really need the most is to use coax for the antenna run and to use a balun at the far end between the antenna (which can be two equal length pieces of wire) and the coax.
That said, you can do better than that with a commercial rabbit ears or with something like a bowtie (or a horizontal variant of a planar disk antenna) A Bowtie is basically two triangles of equal size. They could even be made out of aluminum foil, stuck to a large piece of cardboard with some elmers glue on the back to make it stick. Use two pieces of copper tape to provide a small 'solder-able' area for the feed point.
But make sure to use a balun. To decouple the feed line. (and reduce noise)
The impedance is not that important so a 4:1 balun is fine.
You could even make your own balun if you have some of the right (for VHF/UHF) ferrite cores lying around. But most people over 40 or so usually have a few TV baluns lying around the house. They cost as little as $0.25 on ebay.
There are a bunch of different antenna designs on some of the cordcutter sites.
Are the stations you want to reach all in the same compass direction or scattered all around you?
There are sites where you can get a printout of what directions the stations you want to receive are from you. Having that information would be helpful.
Here are three possible scenarios.
1.) All the stations in the same direction or close.
2.) All the stations in different directions completely.
3. All the stations within 120 degrees of one another and a building behind you that blocks signals from that direction.
Here is a PDF I stumbled upon recently that gives some technical background on the "rabbit ear" type antennas.
https://www.americanradiohistory.com/ARCHIVE-RCA/RCA-Engineer/1975-02-03.pdf So I guess your original idea sounds like a good workable one.
Putting the rabbit ears in the attic on a 75:300 ohm balun and running coaxial cable down to your TV.
You can also find cheap low noise amplifiers if you are in a fringe area.
Under some kinds of long cable run situations an LNA would help a lot. Put it up in the attic between the antenna's balun and the cable. If you do this, make sure to get the kind that uses a signal injector downstairs to feed a low voltage to it.
I have no idea what the quality of units that are sold is but the state of the art in LNA MMICs has improved so much in the last 20 years or so that the chances of getting a decent LNA (for TV use) I think are better now than they ever have been, if you try to be a bit discerning.
In any case they are cheap so it likely wouldn't cost much to try it.
If the rabbit ears are not adequate, you could build any of a large number of very easy to build horizontally polarized antennas which are varying degrees of directional.
Some are really easy to build.
The lowest frequency you need to receive determines the size.
I have one antenna which is basically two triangular patterns that can be cut out of aluminum foil to make a
trapezoidal tooth style log periodic antenna.
They need to be either on two separate pieces of cardboard or on a simgle very large long one that is folded in half that applows the points to meet at the middle.
Tt needs to be fed at its front, where they come to a point ideally with a balun there.
The beauty of this is that the dimensions and variations in the substrate dielectric constant, etc (cardboard or foam core approximates air, i.e. 1) are totally unimportant, if you get the proportions right.
It has 9 or 10 db or so of gain. A lot of gain for something that takes half an hour to make. (For VHF however it would have to be pretty big. Not so practical).
An easy to make antenna could be made out of two pizza tins in a sideways figure eight almost touching, fed right at the middle. That could also work quite well at lower frequencies, indoors and out of sight. the lowest frequency is a bit lower than the two diameters of the pizza tins would be if they were a simple dipole. I forget the exact amount, but I think its around one fifth again, lets say if the dipole was cut for 100 MHz, two pizza tins of identical length would probably work down to 80 MHz. they should be so close they are almost touching and the leads on the balun should be as short as possible. If you have several balun cores you can also use multiple balun cores to increase the baluns effectiveness.
You could also make it into a switchable 1:1 and 1:4 VHF/UHF balun using a (small) DPDT slide switch. That would be useful to have.
http://www.antenna-theory.com/antennas/wideband/log-periodic-dipole.php