No circuits provided at this stage but I will provide the component counts in [ ] brackets.
My ideas are:
TX VXO with a small amount of possible variation using a variable capacitor.
RX would cover a small mybe 20kHz section using a variable capacitor .
TX is a simple vxo mosfet (IRF510 or RD06HHF1) in a colpitts layout [+12] with a minimal lpf [+3] that does double duty as the RX signal goes through the TX lpf. Some XIT is possible as I used a small variable capacitor in series with the the xtal on the ground leg side, if no XIT wanted could remove one component. TX muting is accomplished using a keying circuit and I used a mosfet (2N7000) as the RX mute [+4], turning off he RX feed I would have liked to extend this into the AF chain too as there is a bit of a 'thump' in the audio on change over and I had thought to add a filter but already note component count on RX is high. Test showed 3W out possible from SLA at 12V. No side tone but would make operating for me easier if I used a simple piezo sounder attached to the key/mute circuit [+1]. TX = 
RX seemed to use way too many components and thought this is impossible as I originally started off with a typical BPF [+8] but then realised I had some TOKO coils [+5] then I noted if paid a bit more attention to using the TX LPF and used my MiniVNA and looked carefully at the filter characteristics I could manage to build a high pass filter which in addition to the TX lpf makes up the RX bpf. It is possible to strip the RX filter down to a single TOKO coil and one cap [+3]. Then as this cannot be a DC RX the Rx requires a VFO either a colpitts or pierce, fixed  if using VXO [+11], LC [+11] or varicap [+12]. Anyway this then feeds into the IF chain, for a mixer there are a lot of ways to do this and usually a 602/xtal/602/lm358 would be employed but given the IC count is one and I want to use this in the AF (LM386) and either a switch IC 4066 or 74HC4053 cannot be used as they don't count as switches but with  and  components respectively the option of a DBM [+6] at each end was the first option tried. Now these could either be SBL-1 or similar or FT37-43 and 4 matched 1n4148's I chose the latter. However I looked at other options, using one a transistor (2N2222A) as a mixer [+9], use of a dual gate fet (bf998) [+5], a fet (J310) and PNP (2N39906) [+6]. The detector uses the same configuration as the mixer [+5 to +9], but you could make use of a dual gate fet (bf998) or a fet (j310) and PNP (2N3906) or NPN 2N2222A in a configuration (similar to that which DL6CGC used in the MASter80) where the upper part of the dual gate mosfet acts as the BFO [+9 minimal]. Or you use a separate BFO [detector +9]. The Crystal filter could be made with just a single crystal and two caps [+3] but you have to match the BFO and the one used in the filter closely. For the AF I used my one IC (LM386) [+4] into headphones.
RX = [37 best case].
The power regulation LM7806 or LM7806 uses [+4] or use two battery packs one for 6/8V one for 12V . I would add a reverse protection diode [+1]
Power = 
Anyway... I end up with 61 minimum which cannot be right.....
I have 4, 4.433618, 4.9152, 8, 11.0592 and 20MHz
Another thought... IF the component count is that low... could add a PIC for side tone.... And use an ultra simple AF amp cascading two or three pnp transistors.