I apparently have a bizarre playing style, because I don't run into the economic problem you're having, or at least not to the same scale. I play a custom race, medium economic bonus, no morale bonus. Instead, my points went into tech, soldiering, population growth, and PQ. (IIRC, I don't have it open in front of me.) I also tend to specialize my planets far less than the norm. Nearly all planets will have factories, and all will have starports.
As someone previously stated, do NOT put all factories on your homeworld. That's the economic equivalent of shooting yourself in the foot, but higher up and centered
Instead, build a factory or two, two morale buildings, and economic buildings. Design a custom ship with small hull and a colony module, then crank 3 or 4 of them out. Colonize the first few planets with these, then focus your homeworld on social to finish the buildings. If you really like to micro, on the last turn of each ship you can usually focus social, or turn the military focus off. It buys you a little bit of progress toward whatever you're building from production that would nomally be wasted.
On your first wave colonies, build 2 factories, a lab if there's a bonus, a morale building, and a starport. By the time the starport is done, the population should be high enough to start building colonies from here, leaving your homeworld to increase it's economy in relative peace.
For technology, I start by running up to diplomatic relations, then getting the first factory tech, then the first economic, xeno medicine, xeno entertainment, and from there it varies between games. Trade is completely ignored as an income source (a freighter costs more that early than you could possibly recoup from it in a year or two), but the RoE is necessary.
Other important notes: I play on painful with maxed everything and 7 major races (9 starts you too close to other people). Never put 100% spending into anything at the beginning of the game, I personally choose a 20/20/60 mix and leave it there until I run out of tech to research. Trade goods and other one-off buildings are absolutely vital - very useful for you, but worth even more to deny to your opponents. I usually pick one or two high PQ worlds with at least a 3x manufacturing bonus and crank these things out in 20-30 turns each.
Whatever you do, do not rush to xeno ethics on this big of a map. The various bonuses you can get from choosing evil options during colonization are worth far more than anything you get by declaring neutral (it's been so long, I forgot what bonuses you can get from being neutral). If you choose to go neutral, do so after most of the colonization is done.
A year or two into the game, the economy does go south. Rather than adjust production, simply accept a 200+ bc loss per week as long as possible, then sell tech, trade goods, and anything else you may have to as many civ as you can to prop your economy. Rarely is it necessary to go through more than one or two selling sprees before the economy rebounds. The alternative is to go dark, let your treasury fall until your production shuts off, then alternate a productive turn with a dark turn. Only do this if you are likely to get serious cash in the not-too-distant future.
The major problem with this path is the severe lack of military. Keep an eye on your diplomatic relations, and bribe the two or three most belligerent civs into attacking each other. It's not uncommon for me to have minor civs ranked higher than I am for most of the game.
