Unfortunately this hasn’t worked:
The code used
using PyCall
go = pyimport("plotly.graph_objects")
subplots = pyimport("plotly.subplots")
z1, z2, z3 = rand(7,7),rand(7,7),rand(7,7)
customdata = [z2; z3]
fig = subplots.make_subplots(1, 2, subplot_titles=["z1", "z2"])
fig.add_trace(go.Heatmap(
    z=z1,
    customdata=permutedims(cat(z2,z3; dims=3), (3,1,2)), 
    hovertemplate="<b>z1:%{z:.3f}</b><br>z2:%{customdata[0]:.3f} <br>z3: %{customdata[1]:.3f}",
    coloraxis="coloraxis1", name=""),
    1, 1)
fig.add_trace(go.Heatmap(
    z=z2,
    customdata=permutedims(cat(z1,z3; dims=3), (3,1,2)),
    hovertemplate="z1:%{customdata[0]:.3f} <br><b>z2:%{z:.3f}</b><br>z3: %{customdata[1]:.3f}",
    coloraxis="coloraxis1", name=""),
    1, 2)
fig.update_layout(title_text="Hover to see the value of z1, z2 and z3 together")
fig.show()
fig.write_json("test.json")
 
The json is rather long so I’ve put it in full as a gist, the customdata looks like
"customdata": [
    [
        [
            0.5805209079366938,
            0.4145465488645458,
            0.7488916153892086,
            0.23225747447580458,
            0.6264770747342089,
            0.7567610330366803,
            0.32916084714253446
        ],
        [
            0.2015062562850568,
            0.4135917837269064,
            0.16930646082906786,
            0.1745881009548762,
            0.1325398212462695,
            0.04406350966260275,
            0.5616925298962588
        ],
        [
            0.8159110467216402,
            0.13576374155942017,
            0.08083760578811439,
            0.5201333656078831,
            0.7837785097008303,
            0.14915796393952874,
            0.9400291375195705
        ],
        [
            0.1378231436577635,
            0.5929942496246132,
            0.9473896719538369,
            0.4616840811243895,
            0.5333473566594279,
            0.06172995592070063,
            0.4809335827073493
        ],
        [
            0.37780028857922965,
            0.43308987729445736,
            0.5064184440474073,
            0.725470956444381,
            0.9597526932511722,
            0.6513085078531982,
            0.1340930269426409
        ],
        [
            0.6937839132382566,
            0.5685646057999124,
            0.6104956285971378,
            0.621414306260652,
            0.002360146666188445,
            0.7656254673886753,
            0.26572661925095953
        ],
        [
            0.6409087183731356,
            0.9563299099457475,
            0.5259971837934101,
            0.6615364738436338,
            0.3509257897587722,
            0.3490037963147291,
            0.6629716335118017
        ]
    ],
    [
        [
            0.9649201218864953,
            0.21916662349844673,
            0.5531899995203727,
            0.7448071017070875,
            0.1785674632912978,
            0.10113844840419617,
            0.646186825244371
        ],
        [
            0.5477659883367494,
            0.697919975519172,
            0.16474136212455603,
            0.5012896772774581,
            0.7421155909730657,
            0.2546483235688095,
            0.12312792255812643
        ],
        [
            0.05966905638846021,
            0.27289011490395176,
            0.6990969896823758,
            0.2385454245547438,
            0.40163082837193265,
            0.7756651010814232,
            0.049250699800071684
        ],
        [
            0.7450827999984058,
            0.4845774560680899,
            0.14248259269902008,
            0.9872782254338011,
            0.20457442522269187,
            0.28431787691554167,
            0.02056202670215379
        ],
        [
            0.07378521255490389,
            0.0013557371016771347,
            0.459154954303597,
            0.2871300415587916,
            0.5683161887752379,
            0.25049146125235866,
            0.11849448778617544
        ],
        [
            0.08423470866345806,
            0.9999795922545266,
            0.8910123710017198,
            0.9415311112476029,
            0.822896594704122,
            0.7202498051568375,
            0.05499178822187689
        ],
        [
            0.3359137070920404,
            0.575472993955267,
            0.2270050158557153,
            0.09613539197838517,
            0.2835117001116986,
            0.1177908924733897,
            0.8270291410302797
        ]
    ]
],
Hopefully this is what you meant 